Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993 Footnote^∗

^∗Research partially sponsored by the Office of Naval Research under Contract N00014-89-5-1537.

References

• Ablow , C.W. and Brigham , G. 1955 . An analog solution of programming problems . Oper. Res , 3 : 388 – 394 .
   Web of Science ®Google Scholar
• Adler , I. , Karmarkar , N. , Resende , M.G.C. and Veiga , G. 1989 . An implementation of Karmarkar’s algorithm for linear programming . Math. Prog , 44 : 297 – 335 .
   Web of Science ®Google Scholar
• Adler , I. and Monteiro , R.D.C. 1991 . Limiting behavior of the affine scaling continuous trajectories for linear programming problems . Math. Prog , 50 : 29 – 51 .
   Web of Science ®Google Scholar
• Afimiwala K. A. Program package for design optimization State University of New York Buffalo 1974 Department of Mechanical Engineering
   Google Scholar
• Alart , P. and Lemaire , B. 1991 . Penalization in non-classical convex programming using variational convergence . Math. Prg , 51 : 307 – 331 .
   Web of Science ®Google Scholar
• Al-Sultan , K.S. and Murty , K.G. 1992 . A scaling technique for finding the weighted analytic center of a polytope . Math. Prog , 57 : 145 – 161 .
   Web of Science ®Google Scholar
• Anstreicher , K.M. 1986 . A monotonic projective algorithm for fractional linear programming . Algorithmica , 1 : 483 – 498 .
   Web of Science ®Google Scholar
• Anstreicher , K.M. 1987 . Linear Programming and the Newton Barrier Flow , New Haven, CT : Yale School of Organization and Management . Box 1A, 06520
   Google Scholar
• Anstreicher , K.M. 1989 . A combined ‘Phase I-Phase 11’ Projective algorithm for linear programming . Math. Prog , 43 : 209 – 223 .
   Web of Science ®Google Scholar
• Anstreicher K. M. On long step path following and SUMT for linear and quadratic programming Yale University New Haven 1990 Technical Paper, Department of Operations Research, Connecticut 06520
   Google Scholar
• Anstreicher , K.M. 1991 . Dual ellipsoids and degeneracy in the projective algorithm for linear programming . Contemporary Math , 114 : 141 – 150 .
   Google Scholar
• Armacost , R.L. and Fiacco , A.V. 1974 . Sensitivity analysis for NLP programming . Math. Prog , 6 : 301 – 326 .
   Google Scholar
• Armacost R. L. Fiacco A. V. Second Order Parametric Sensitivity Analysis in NLP and Estimates by Penalty Function Methods The George Washington University 1975 Washington, D.C Technical Paper T-324, Institute for Management Science and Engineering
   Google Scholar
• Armacost R. L. Mylander W. C. A guide to SUMT-Version 4 computer subroutine for implementing sensitivity analysis in nonlinear programming The George Washington University Washington, D.C 1973 Technical Paper T-287, The Institute for Management Science and Engineering
   Google Scholar
• Atkinson , D.S. and Vaidya , P.M. 1992 . A scaling technique for finding the weighted analytic center of a polytope . Math. Prog , 57 : 163 – 193 .
   Web of Science ®Google Scholar
• Auslender , A. 1970 . Recherche des points de selle d’une function . CCERO , 12 : 57 – 75 .
   Google Scholar
• Auslender , A. 1979 . Penalty methods for computing points that satisfy S.O.N.C . Math. of O.R , 17 : 229 – 238 .
   Google Scholar
• Bandler , J.W. and Charalambous , C. 1974 . Nonlinear programming using minimax techniques . J.O.T.A , 13 : 607 – 619 .
   Web of Science ®Google Scholar
• Barnes , E.R. 1986 . A variation of Karmarkar’s algorithm for solving linear programming problems . Math. Prog , 36 : 174 – 182 .
   Web of Science ®Google Scholar
• Barnes , E.R. , Chopra , S. and Jensen , D.L. 1988 . “ A Polynomial Time Version of the Affine Scaling Algorithm ” . In Graduate Schood of Business Adminitsration , New York : New York University . Working Paper
   Google Scholar
• Bartels , R.H. 1980 . A Penalty Linear Programming Method Using Reduced-Gradient Basis- Exchange Techniques in Linear Algorithms and its Applications . Linear Algebra and its Applications , 29 : 17 – 32 .
   Web of Science ®Google Scholar
• Bartholomew-Biggs M. C. An Improved Implementation of the Recursive Quadratic Programming Method for Constrained Minimization The Hatfield Polytechnic Hatfield, , England 1979 Technical Report No 105, Numerical Optimisation Center
   Google Scholar
• Bayer , D.A. and Lagarias , J.C. 1986 . The Nonlinear Geometry of Linear Programming , Murray Hill, NJ : AT & T Bell Laboratories . Perprints
   Google Scholar
• Bellmore , M. , Greenberg , H.J. and Jarvis , J.J. 1968 . Generalized penalty-function concepts in mathematical optimization . Oper. Res , 18 : 229 – 252 .
   Web of Science ®Google Scholar
• Ben-Daya , M. and Shetty , C.M. 1988 . Polynomial Barrier Function Algorithms for Linear Programming , Atlanta, GA : Georgia Institute of Technology . School of Industrial and Systems Engineering, 30332-0205
   Google Scholar
• Bergounioux , M. 1993 . Augmented Lagrangian method for distributed optimal control problems with State Constraints . J.O.T.A , 78 : 493 – 521 .
   Web of Science ®Google Scholar
• Bertsekas , D.P. . Convergence rate ofpenalty and multipliers methods . Proc. 1973 IEEE Confer. Decision Control . San Diego, CA. pp. 260 – 264 .
   Google Scholar
• Bertsekas , D.P. 1975 . Combined primal-dual and penalty methods for constrained minimization . SIAM J. on Control , 13 : 521 – 544 .
   Web of Science ®Google Scholar
• Bertsekas , D.P. 1975 . Necessary and sufficient conditions for a penalty function to be exact . Math. Prog , 9 : 87 – 99 .
   Web of Science ®Google Scholar
• Bertsekas , D.P. 1975 . “ On Penalty and Multiplier Methods for Constrained Minimization ” . In Nonlinear Programming Edited by: Mangasarian , O.L. , Meyer , R.R. and Robinson , S.M. Vol. 2 , 165 – 191 .
   Google Scholar
• Bertsekas , D.P. 1977 . Approximation procedures based on the method of multipliers . J.O.T.A , 23 : 487 – 510 .
   Web of Science ®Google Scholar
• Bertsekas , D.P. 1982 . Constrained Optimization and Lagrange Multiplier Methods , London, New York : Academic Press .
   Google Scholar
• Best , M.J. 1975 . A feasible conjugate direction method to solve linearly constrained optimization problems . J.O.T.A , 16 : 25 – 38 .
   Web of Science ®Google Scholar
• Best , M.J. and Ritter , K. 1976 . A class of accelerated conjugate direction methods for linearly constrained minimization problems . Math Computation , 30 : 478 – 504 .
   Web of Science ®Google Scholar
• Betts , J.T. 1975 . An improved penalty function method for solving constrained parameter optimization problems . J.O.T.A , 16 : 1 – 24 .
   Web of Science ®Google Scholar
• Betts , J.T. 1977 . An accelerated multiplier method for nonlinear programming . J.O.T.A , 21 : 137 – 174 .
   Web of Science ®Google Scholar
• Bhatt , S.K. 1973 . Sequential unconstrained minimization technique for non-convex program . CCERO , 15 : 429 – 435 .
   Google Scholar
• Birge , J.R. and Qi , L. 1988 . Computing block-angular Karmarkar projections with applications to stochastic programming . Man. Scien , 34 : 1472 – 1479 .
   Web of Science ®Google Scholar
• Blair , C.E. and Jeroslow , R.G. 1981 . An exact penalty method for mixed-integer programs . Math. of O.R , 6 : 14 – 18 .
   Web of Science ®Google Scholar
• Boggs P. T. Domich P. D. Donaldson J. R. Algorithmic Enhancement to the Method of Centers for Linear Programming Problems 1988
   Google Scholar
• Boggs , P.T. and Tolle , J.W. 1980 . Augmented Lagrangian which are quadratic in the multiplier . J.O.T.A , 31 : 17 – 26 .
   Web of Science ®Google Scholar
• Boukari , D. September 1990 . Non-algorithmic Sensitivity Analysis and Tolerance Bounds in Linear and Nonlinear Programming , September , Washington : The George Washington University . D.C, Ph.D. Dissertation
   Google Scholar
• Bracken , J. and McGill , J.T. 1974 . A method for solving mathematical programming with nonlinear programs in the constraints . Oper. Res , 22 September : 1097 – 1101 .
   Web of Science ®Google Scholar
• Breitfeld M. G. Shanno D. F. Computational Experience with Modified Log-barrier Functions for Nonlinear Programming Rutgers University New Brunswick, New Jersey 1993 RUTCOR Research Report RRR 17–93, Rutgers Center for Operations Research. Submitted to Annals of Operations Research
   Google Scholar
• Burke , J.V. 1991 . An exact penalization viewpoint of constrained optimization . SIAM J. on Control and Optim , 29 September : 968 – 998 .
   Web of Science ®Google Scholar
• Butler , T. and Martin , A.V. 1962 . On a method of Courant for minimizing functionals . J. Math. and Physics , 41 September : 291 – 299 .
   Web of Science ®Google Scholar
• Buys , J.D. 1972 . Dual Algorithms for Constrained Optimization , Rijksuniversiteit de Leiden . Ph.D. Thesis
   Google Scholar
• Camp , G.D. 1955 . Inequality-constrained stationary value problems . J. Oper. Res. Soc. Am , 3 : 548 – 550 .
   Web of Science ®Google Scholar
• Carotenuto , L. and Raiconi , G. 1987 . On the minimization of quadratic functions with bilinear constraints via augmented Lagrangian . J.O.T.A , 55 : 23 – 36 .
   Web of Science ®Google Scholar
• Carroll , C.W. 1961 . The created response surface technique for optimizing nonlinear restrained systems . Oper. Res , 9 : 169
   Web of Science ®Google Scholar
• Censor , Y. and Lent , A. 1987 . Optimization of ‘x log x’ entropy over linear equality constraints . SIAM J. on Control and Optim , 25 : 921 – 933 .
   Web of Science ®Google Scholar
• Charalambous , C. 1978 . A lower bound for the controlling parameters of the exact penalty functions . Math. Prog , 15 : 278 – 290 .
   Web of Science ®Google Scholar
• Charalambous , C. 1980 . A method to overcome the ill-conditioning problem of differentiable penalty functions . Oper. Res , 28 : 650 – 667 .
   Web of Science ®Google Scholar
• Choi , I.C. and Goldfarb , D. 1992 . Exploiting special structure in a primal-dual path-following algorithm . Math. Prog , 58 : 33 – 52 .
   Web of Science ®Google Scholar
• Coleman , T.F. and Conn , A.R. 1980 . Second order conditions for an exact penalty function . Math. Prog , 19 : 178 – 185 .
   Web of Science ®Google Scholar
• Coleman , T.F. and Conn , A.R. 1980 . “ Nonlinear programming via an exact penalty function:asymptotic analysis ” . In Compt. Sci. Dep. Rep. CS , Vol. 80-30 , University of Waterloo .
   Google Scholar
• Coleman , T.F. and Conn , A.R. 1980 . “ Nonlinear programming via an exact penalty function: global analysis ” . In Compt. Sci. Dep. Rep. CS , Vol. 80-31 , University of Waterloo .
   Google Scholar
• Colville , A.R. 1968 . A comparative study of nonlinear programming codes , NY : IBM Scientific Center . Report 320-2949
   Google Scholar
• Conn , A.R. 1979 . LP via a non-differentiable penalty function . SIAM J. of Numerical Analysis , 13 : 196 – 208 .
   Google Scholar
• Cottle , R.W. and Dantzig , G.B. 1968 . Complementary pivot theory of mathematical programming . Linear Algebra and its Applications , 1 : 103 – 125 .
   Google Scholar
• Courant , R. 1943 . Variational methods for the solution of problems of equilibrium and vibrations . Bull. Amer. Math. Soc , 49 : 1 – 23 .
   Google Scholar
• Dantzig , G.B. 1963 . Linear Programming and Extensions , Princeton, New Jersey : Princeton University Press .
   Google Scholar
• Dantzig , G.B. and Wolfe , P. 1961 . The decomposition algorithm for linear programming . Econometrica , 29 : 767 – 778 .
   Web of Science ®Google Scholar
• Ghellinck , G. and Vial , J.P. 1961 . A polynomial Newton method for linear programming . Algorithmica , 1 : 425 – 453 .
   Web of Science ®Google Scholar
• Ghellinck , G. and Vial , J.P. 1987 . An extension of Karmarkar’s algorithm for solving a system of linear homogeneous equations on the simplex . Math. Prog , 39 : 79 – 92 .
   Web of Science ®Google Scholar
• Dembo , R.S. 1976 . A set of geometric programming test problems and their solutions . Math. Prog , 10 : 192 – 213 .
   Web of Science ®Google Scholar
• Dembo , R.S. 1978 . Current state of the art of algorithms and computer software for geometric programming . J.O.T.A , 26 : 149 – 183 .
   Web of Science ®Google Scholar
• Den Hertog , D. and Roos , C. 1991 . A survey of search directions in interior point methods for linear-programming . Math. Prog , 52 : 481 – 509 .
   Web of Science ®Google Scholar
• Den Hertog , D. , Roos , C. and Terlaky , T. 1992 . A potential reduction method for a class of smooth convex programming problems . SIAM J. on Optim , 2
   Web of Science ®Google Scholar
• Den Hertog , D. , Roos , C. and Terlaky , T. 1992 . On the classical logarithmic barrier function methodfor a class of smooth convex programming problems . J.O.T.A , 73 : 1 – 25 .
   Web of Science ®Google Scholar
• De , O. , Pantoja , J.F.A. and Mayne , D.Q. 1991 . Exact penalty function algorithm with simple updating of the penalty parameter . J.O.T.A , 69 : 441 – 467 .
   Web of Science ®Google Scholar
• de Silva A. H. Sensitivity Formulas for Nonlinear Factorable Programming and their Application to the Solution of an Implicitly Defined Optimization Model of U.S. Crude Oil Production George Washington University Washington, D.C 1978 Ph.D. Dissertation, School of Engineering and Applied Science
   Google Scholar
• De Silva , A.H. and McCormick , G.P. 1992 . Implicitly defined optimization problems . Annals of O.R , 34 : 107 – 124 .
   Google Scholar
• Dikin , I.I. 1967 . Iterative solution of problems of linear and quadratic programming . Soviet Mathematics Doklady , 8 : 674 – 675 .
   Google Scholar
• Dikin , I.I. 1974 . On the speed of an iterative process . Upraylyaemye Sistemi , 12 : 54 – 60 . In Russian
   Google Scholar
• Di Pillo , G. and Grippo , L. 1979 . A new class of augmented Lagrangian in nonlinear programming . SIAM J. on Control and Optim , 17 : 618 – 628 .
   Web of Science ®Google Scholar
• Di Pillo , G. and Grippo , L. 1982 . A new augmented Lagrangian function for inequality constraints in nonlinear programming problems . J.O.T.A , 36 : 495 – 519 .
   Web of Science ®Google Scholar
• Di Pillo , G. and Grippo , L. 1986 . An exact penalty function method with global convergence properties for NLP problems . Math. Prog , 36 : 1 – 18 .
   Web of Science ®Google Scholar
• Di Pillo , G. and Grippo , L. 1988 . On the exactness of a class of nondifferentiable functions . J.O.T.A , 57 : 399 – 410 .
   Web of Science ®Google Scholar
• Easton , E.D. 1977 . “ Validity of Colville’s time standardization for comparing optimization codes ” . In ASME Des. Eng. Tech. Con$ Paper No 77-DET-116 Chicago
   Google Scholar
• Easton , E.D. and Fenton , R.G. 1974 . A comparison of numerical optimization methods for engineering design . Trans. ASME Ser. B , 96 : 196 – 200 .
   Google Scholar
• Engersbach , N.H. . Implementation of Variable Metric Method for Constrained Optimization Based on an Augmented Lagrangian Functional . Lecture Notes in Computer Science No 27, Optimization Techniques IFIP Technical Conference . Edited by: Goos , G. and Hartmams , J. pp. 291 – 302 .
   Google Scholar
• Ermoliev , Y.M. and Shor , N.Z. 1967 . On the minimization of nondifferentiable functions . Kibernetika (Kiev) , 3 : 101 – 102 .
   Google Scholar
• Fattler , J.E. , Sin , Y.T. , Root , R.R. , Ragsdell , K.M. and Reklaitis , G.V. 1982 . On the computational utility of posynomial geometric programming solution methods . Math. Prog , 22 : 163 – 201 .
   Web of Science ®Google Scholar
• Ferris , M.C. and Philpott , A.B. 1989 . An interior point algorithm for semi-infinite linear programming . Math. Prog , 43 : 257 – 276 .
   Web of Science ®Google Scholar
• Ferris , M.C. and Philpott , A.B. 1992 . On affine scaling and semi-infinite linear programming . Short Communication, Math. Prog , 56 : 361 – 364 .
   Web of Science ®Google Scholar
• Fiacco , A.V. June 1967 . Sequential Unconstrained Minimization Methods for Nonlinear Programming , Vol. III , June , Evanston : Northwestern University . Ph.D. Dissertation
   Google Scholar
• Fiaco , A.V. 1970 . Penalty methods for mathematical programming in E n with general constraint sets . J.O.T.A , 6 June : 252 – 268 .
   Google Scholar
• Fiacco , A.V. 1976 . Sensitivity analysis for nonlinear programming using penalty methods . Math. Prog , 10 June : 287 – 311 .
   Web of Science ®Google Scholar
• Fiacco , A.V. 1983 . Introduction to Sensitivity Analysis in Nonlinear Programming , New York : Academic Press .
   Google Scholar
• Fiacco , A.V. 1987 . “ Projective SUMT is a Perturbed Variation of Classical SUMT ” . In Technical Paper 520/87 , Washington : The George Washington University . School of Engineering and Applied Science.DC 200052
   Google Scholar
• Fiacco , A.V. and Jones , A.P. 1969 . Generalized penalty methods in topological spaces . SIAM J. Appl. Math , 17
   Web of Science ®Google Scholar
• Fiacco A. V. McCormick G. P. Programming Under Nonlinear Constraints by Unconstrained Minimization: A Primal-Dual Method Research Analysis Corporation McLean, Virginia 1963 Technical Paper RAC-TP-96
   Google Scholar
• Fiacco , A.V. and McCormick , G.P. 1965 . SUMT without Parameters, System Research Memorandom No. 121 , Vol. III , Evanston : Technical Institute, Northwestern University .
   Google Scholar
• Fiacco , A.V. and McCormick , G.P. 1968 . Nonlinear Programming: Sequential Unconstrained Minimization Technique , New York : John Wiley & Sons . (Republication published by SIAM in a series called Classics in Applied Mathematics,1990)
   Google Scholar
• Fletcher , R. 1970 . A new approach to variable metric algorithms . computer J , 13 : 317 – 322 .
   Web of Science ®Google Scholar
• Fletcher , R. 1970 . A Class of Methods for Nonlinear Programming with Termination and Convergence Properties, in Integer and Nonlinear Programming , Edited by: Abadie , J. 157 – 173 . Amsterdam : North-Holland Publ .
   Google Scholar
• Fletcher , R. 1973 . An exact penalty function for nonlinear programming with inequalities . Math. Prog , 5 : 129 – 150 .
   Google Scholar
• Fletcher , R. 1973 . An Ideal Penalty Function for Constrained Optimization, HL 74/66 , England : AERE Harwell .
   Google Scholar
• Fletcher , R. and Lill , S. 1971 . “ A Class of Methods for Nonlinear Programming: II ” . In Computational Experience,in Nonlinear Programming , Edited by: Rosen , J.B. , Mangasarian , O.L. and Ritter , K. 67 – 92 . New York : Academic Press .
   Google Scholar
• Frank , M. and Wolfe , P. 1956 . An algorithm for quadratic programming . Naval Research Quarterly , 3 : 95 – 110 .
   Google Scholar
• Freund R. M. Projective Transformation for Interior-Point Algorithms, and a Superlinearly Convergent Algorithm for the W-Center Problem 1989 Technical Report
   Google Scholar
• Frank , R.M. and Tan , K.C. 1991 . A method for the parametric center problem, with a strictly monotone polynomial-time algorithm for linear programming . Math of O.R , 46 : 775 – 801 .
   Google Scholar
• Frisch , K.R. 1954 . “ Principles of Linear Programming with Particular Reference to the Double Gradient Form of the Logarithmic Potential Method ” . In Memo of Oct , Oslo : University Institut of Economics .
   Google Scholar
• Gabriele , G.A. and Ragsdell , K.M. 1977 . OPTILIB User’s Manual , Purdue University .
   Google Scholar
• Gamble , A.B. , Conn , A.R. and Pulleyblank , W.R. 1991 . A network penalty method . Math Prog , 50 : 53 – 73 .
   Web of Science ®Google Scholar
• Gagnon , C.R. 1974 . Nonlinear programming approach to a very large hydroelectric system optimization . Math Prog , 6 : 28 – 41 .
   Google Scholar
• Gay , D.M. 1987 . A variant of Karmarkar's linear programming algorithm for problems in standard form . Math Prog , 37 : 81 – 90 .
   Web of Science ®Google Scholar
• Gay , D.M. 1989 . Stopping Tests that Compute Optimal Solution for Interior-Point Linear Programming Algorithm, Numerical Analysis Manuscript 89-11 , Murray Hill, NJ : AT & T Bell Labs .
   Google Scholar
• Giannessi , F. 1984 . J.O.T.A , 42 : 331 – 365 .
   Web of Science ®Google Scholar
• Gill , P.E. 1974 . Numerical Methods for Constrained Optimization , Edited by: Murray , W. New York : Academic Press .
   Google Scholar
• Gill P. E. Murray W. Saunders M. A. Tomlin U. A. Wright M. H. The Design and Structure of a Fortran Program Library for Optimization Stanford University Stanford, CA 1977 Technical Report SOL77-7 Systems Optimization Laboratory
   Google Scholar
• Gill P. E. Murray W. Saunders M. A. Tomlin J. A. Wright M. H. User's Guide for SOL/NPSOL, A Fortran Package for Nonlinear Programming Stanford University CA 1983 Report Sol 83-12, Department of Operation Research
   Google Scholar
• Gill , P.E. , Murray , W. , Saunders , M.A. , Tomlin , J.A. and Wright , M.H. 1986 . On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method . Math Prog , 36 : 183 – 209 .
   Web of Science ®Google Scholar
• Gill P. E. Murray W. Saunders M. A. Tomlin J. A. Wright M. H. Department of Operations Research Stanford, California 1986 A Note on Nonlinear Approaches to Linear Programming, Technical Report SOL 86-7, Systems Optimization Laboratory, 94304-4022
   Google Scholar
• Glad , S.T. 1979 . Properties of updating methods for the multipliers in augmented Lagrangian . JOTA , 28 : 135 – 156 .
   Web of Science ®Google Scholar
• Goffin , J.L. 1988 . “ Affine and Projective Transformation in Non-Differentiable Optimization, in Trends in Mathematical Optimization ” . In International Series of Numerical Mathematics No 84 , Edited by: Hoffmann , K.H. , Hiriart-Urruty , J.B. , Lemarechal , C. and Zowe , J. 460 – 472 . Baset Boston : Birkhauser .
   Google Scholar
• Goffin J. L. Haurie A. Vial J. P. Decomposition and Nondifferentiable Optimization with the Projective Algorithm McGill University Montreal, Quebec 1990 Technical Report 91-01-17, Faculty of Management
   Google Scholar
• Goffin , J.L. and Vial , J.P. 1990 . Cutting plane and column generation techniques with the projective algorithm . JOTA , 65 : 409 – 429 .
   Web of Science ®Google Scholar
• Goldfart , D. and Liu , S. 1991 . On o(n 3 l) Primal interior point algorithm for convex quadratic programming . Math Prog , 49 : 325 – 340 .
   Web of Science ®Google Scholar
• Goldfarb , D. and Todd , M.J. 1990 . Linear programming optimization , Edited by: Nemhauser , G.L. , Rinnooy Kan , A.H.G. and Todd , M.J. Amsterdam : North-Holland . Holland
   Google Scholar
• Gonzaga C. C. Polynomial Affine Algorithms for Linear Programming Report Universidade Federal do Rio de Janeiro Rio de Janeiro, , Brazil 1988 ES-139188 COPPE
   Google Scholar
• Gonzaga , C.C. 1988 . Conical projection algorithm for linear programming . Math. Prog , 43 : 151 – 173 .
   Web of Science ®Google Scholar
• Gonzaga , C.C. 1989 . An Algorithm for Solving Linear Programs in o(n ₃ L) Operations, in Progress in Mathematical Programming , Edited by: Megiddo , N. 1 – 28 . Berlin, , Germany : Springer-Verlag .
   Google Scholar
• Gonzaga C. C. Large-Steps Path-Following Methods for Linear Programming: Potential Reduction Method COPPE-Federal University of Rio de Janeiro Rio de Janeiro 1989 Internal Report ES-211189
   Google Scholar
• Gongzaga , C.C. 1991 . Large-Steps Path-Following Method in Linear Programming: Barrier Function Method . SIAM Journal on Optim , 1
   Web of Science ®Google Scholar
• Gonzaga , C.C. 1992 . Path following methods for linear programming . SIAM Review , 34 : 167 – 224 .
   Web of Science ®Google Scholar
• Güeler , O. 1993 . Existence of interior points and interior paths in nonlinear monotone complementarity problems . Math. of O.R , 18 : 128 – 147 .
   Web of Science ®Google Scholar
• Gulf Oil Coporation . 1972 . COMPUTEII. A General Purpose Optimizer for Continuous Nonlinear Models-Description and User’s Manual , Houston, TX : Gulf Computer Sciences .
   Google Scholar
• Gwinner , J. “ On the Penalty Method for Constrained Variational Inequalities in Lecture Notes in Pure and Applied Mathematics No 86, Optimization ” . In Theory and Algorithms Edited by: Hiriart Urruty , J.B. , Oettli , W. and Stoer , J. 197 – 211 .
   Google Scholar
• Haarhoff , P.C. and Buys , J.D. 1970 . A new method for the optimization of a nonlinear function subject to nonlinear constraints . Computer J , 13 : 178 – 184 .
   Web of Science ®Google Scholar
• Han , S.P. 1979 . Penalty Lagrangian methods via a quasi-Newton approach . Math of O.R , 4 : 291 – 302 .
   Google Scholar
• Han , S.P. and Mangasarian , O.L. 1979 . Exact penalty function in nonlinear programming . Math. Prog , 17 : 251 – 269 .
   Web of Science ®Google Scholar
• Han , S.P. and Mangasarian , O.L. 1983 . Math Prog , 25 : 293 – 306 .
   Web of Science ®Google Scholar
• Hartman , J.K. 1975 . JOTA , 16 : 49 – 66 .
   Web of Science ®Google Scholar
• Hesten , M.R. 1969 . J.O.T.A , 4 : 303 – 320 .
   Google Scholar
• Howe , S. 1974 . Man. Scien , 21 : 341 – 347 .
   Web of Science ®Google Scholar
• Huard , P. 1967 . Resolution of Mathematical Programming with Nonlinear Constraints by the Methods of Centers, in Nonlinear Programming , Edited by: Abadie , J. 209 – 219 . Amsterdam : Noth Holand .
   Google Scholar
• Indusi , J.P. 1972 . A Computer Algorithm for Constrained Minimization Algorithms , Edited by: Szego , G.P. London : Academic Press .
   Google Scholar
• Jarre F. TheMethod of Analytic Centersfor Smooth Convex Programs Universität Würzburg Würzburg, , Germany 1989 Ph.D. Thesis, Institute für Angewandte Mathematik und Statistik
   Google Scholar
• Jarre , F. 1991 . On the convergence of the method of analytic centers when applied to convex quadratic programs . Math.Prg , 49 : 341 – 358 .
   Web of Science ®Google Scholar
• Jittorntrum , K. and Osborne , M.R. 1978 . rajectory analysis and extrapolation in barrier function methods . J.Austral. Math.Soc , 20 : 352 – 369 . Series B
   Google Scholar
• Kapoor , S. and Vaidya , P. 1986 . Fast Algorithm for Convex Quadratic Programming and Multicommodity Flows . Proceedings of the 18th Annual ACM Symposium on the Theory of Computing . 1986 . pp. 147 – 159 .
   Google Scholar
• Karmarkar , N. 1984 . A new polynomial-time algorithm for linear programming , Murray Hill, New Jersey : A. T. & T.Laboratories . 07974
   Google Scholar
• Karmarkar , N. , Resende , M.G.C. and Ramakrishnan , K.G. 1991 . An interior point algorithm to solve computationaly difficult set covering problems . Math. Prog , 52 : 597 – 618 .
   Web of Science ®Google Scholar
• Khachiyan , L.G. 1979 . A polynomial algorithm in linear programming . Nauk D.A. SSSR , 24 : 1093 – 1096 . Translated in Sorjiet Mathematics-Doklady, (20)1, 191-194
   Google Scholar
• Kojima , M. , Megiddo , N. and Ye , Y. 1992 . An interior point potential reduction algorithm for the linear complementarity problem . Math, Prog , 54 : 267 – 279 .
   Web of Science ®Google Scholar
• Kojima , M. , Mizuno , S. and Noma , T. 1990 . Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems . Math of O.R , 15 : 662 – 675 .
   Web of Science ®Google Scholar
• Kojima , M. , Mizuno , S. and Yoshise , A. 1989 . “ A Primal-Dual Interior-Point Algorithm for Linear Programming ” . In Progress in Mathematical Programming , Edited by: Megiddo , N. 29 – 48 . Berlin, , Germany : Springer- Verlag .
   Google Scholar
• Kojima , M. , Mizuno , S. and Yoshise , A. 1989 . A polynomial-time algorithm for a class of linear complementary problems . Math. Prog , 44 : 1 – 26 .
   Web of Science ®Google Scholar
• Kojima , M. , Mizuno , S. and Yoshise , A. 1991 . An 0(n 1/2 L)iterations potential reduction algorithm for linear complementarity problems . Math.Prog , 50 : 331 – 342 .
   Web of Science ®Google Scholar
• Kort , B.W. 1975 . Rate of Convergence of the Method of Multipliers With Inexact Minimization in Nonlinear Programming 2 Edited by: Mangasarian , 0.L. , Meyer , R.R. and Robinson , S.M. 193 – 214 .
   Google Scholar
• Kort , B.W. and Bertsekas , D.P. . A New Penalty Function Method for Constrained Minimization . In Proceedings of 1972 IEEE Conference on Decision and Control . New Orleans. pp. 162 – 166 .
   Google Scholar
• Kortanek , K.0. and No , H. 1992 . A second order affine scaling algorithm for the geometric programming dual with logarithmic barrier . Optimization , 23 : 303 – 322 .
   Google Scholar
• Kortanek , K.O. , Potra , F. and Ye , Y. 1991 . On some efficient interior point methods for nonlinear convex programming . Linear Algebra and Its Applications , 152 : 169 – 189 .
   Web of Science ®Google Scholar
• Kortanek , K.0. and Zhu , J. 1993 . A polynomial barrier algorithm for linearly constrained convex programming problems . Mathematics of Operations Research , 18 : 116 – 127 .
   Web of Science ®Google Scholar
• Kortanek K. O. Zhu J. On Controlling the Parameter in the Logarithmic Barrier Term for Convex Programming Problems The University of Iowa Iowa City, Iowa 1993 Technical Report, Department of M.S., College of Business Adminitsration, to appear in JOTA
   Google Scholar
• Kraft D. Nichtlineare Programming-Grundlagen 1977 Verfohren, Beispiele, Forschingsbericht, DFVLR, Oberpfofenhofen, West Germany
   Google Scholar
• Lasdon , L.S. 1972 . An efficient algorithm for minimizing barrier and penalty functions . Math.Prog , 2 : 65 – 106 .
   Google Scholar
• Lasdon , L.S. and Waren , A.D. 1979 . The status of nonlinear programming software . Oper.Res , 27 : 431 – 456 .
   Web of Science ®Google Scholar
• Lasdon , L.S. , Fox , R.L. and Ratner , M.W. 1973 . An efficient one dimensional search procedure for barrier functions . Math.Prog , 4 : 279 – 296 .
   Google Scholar
• Lehmkuhl L. A Polynomial Primal-Dual Interior Point Method for Convex Programming with Quadratic Constraints George Washington University Washington, D.C. 1993 Ph.D. Dissertation, Department of Operations Research
   Google Scholar
• Lill S. E04HAF User's Guide The University of Liverpool Computer Laboratory 1974 Numerical Algorithm Group Document No 737
   Google Scholar
• Lootsma , F.A. 1977 . “ The ALGOL 60 Procedure Minifun for Solving Nonlinear Optimization Problems ” . In Technical Report Dept.of Mathematics , Delft, , Netherlands : University of Technology .
   Google Scholar
• Lootsma , F.A. 1980 . “ Ranking of Nonlinear Optimization Codes According to Efficiency and Robustness ” . In In Konstruktive Methoden der Finitien Nichtlinear optimierung , Edited by: Collatz , L. , Meinardus , G. and Wetterling , W. 157 – 158 . Basel, , Switzerland : Birkhauser .
   Google Scholar
• Lucidi , S. 1990 . Recursive cluadratic programming algdrithm that uses an exact augmented Lagrangian function . J.O.T.A , : 227 – 231 .
   Web of Science ®Google Scholar
• Luenberger , D.G. 1970 . Control problems with kinks . IEEE Trans.Automat.Control , 15 : 570 – 575 .
   Google Scholar
• Luenberger , D.G. 1971 . Convergence rate of a penalty-function scheme . J.O.T.A , 7 : 39 – 51 .
   Google Scholar
• Luenberger , D.G. 1974 . A combined penalty function and gradient projection method for nonlinear programming . J.O.T.A , 14 : 477 – 495 .
   Web of Science ®Google Scholar
• Martsen , R.E. 1987 . The IMP System on Personal Computers . presentation given at ORSA/TIMS Joint National Meeting . 1987 , MO. St.Louis .
   Google Scholar
• Martsen , R.E. , Saltzman , M.J. , Shanno , D.F. , Pierce , G.S. and Ballinttijn , J.F. 1988 . Implementation of a Dual Affine Interior Algorithm for Linear Programming , Tucson, , AZ : University of Arizona . Working Paper CMI-WPS-88-06
   Google Scholar
• Masuzawa , K. , Mizuno , S. and Mori , M. 1990 . A polynomial time interior point algorithm for minimum cost flow problems . J.of the Oper.Res.Society of Japan , 33 : 157 – 167 .
   Google Scholar
• Mayne , D.Q. and Maratos , N. 1979 . A first order exact penalty function algorithm for equality constrained optimization problems . Math.Prog , 16 : 303 – 324 .
   Web of Science ®Google Scholar
• McCormick , G.P. 1971 . Penalty function versus non-penalty function methods for constrained nonlinear programming problems . Math.Prog , 1 : 217 – 238 .
   Google Scholar
• McCormick G. P. A Mini Manual for Use of the Sumt Computer Program and the Factorable Programming Language Stanford University 1974 Department of Operations Research, Systems Optimization Laboratory Technical Report SOL-74-15, Stanford California
   Google Scholar
• McCormick , G.P. 1978 . An idealized penalty function, in nonlinear programming 3 , Edited by: Mangasarian , 0.L. , Meyer , R.R. and Robinson , S.M. 165 – 195 . New York : Academic Press .
   Google Scholar
• McCormick G. P. The Discrete Projective SUMT Method for Convex Programming The George Washington University Washington, DC 1986 Technical Paper 509186 , School of Engineering and Applied Science, 20052
   Google Scholar
• McCormick G. P. Miscellaneous Results Conerning Karmarkar's Projective Method and SUMT The George Washington University Washington, DC 1987 Technical Paper 519187, School of Engineering and Applied Science, 20052
   Google Scholar
• McCormick G. P. The Superlinear Convergence of a Nonlinear Primal-Dual Algorithm George Washington University Washington, DC 1991 Technical Paper T-550191, Department of Operations Research
   Google Scholar
• McCormick G. P. Mylander III W. C. Fiacco A. V. Computer Program Implementing the Sequential Unconstrained Minimization Technique for Nonlinear Programming Research Analysis Corporation McLean, Virginia 1965 Technical Paper RAC-TP-151
   Google Scholar
• McCormick G. P. Witzgall C. Primal-Dual Convergence of Continuous Interior Point Methods for Convex Programming The George Washington University 1988 Draft Technical Report
   Google Scholar
• Megiddo , N. 1989 . “ Pathways to the Optimal Set in Linear Programming ” . In Progress in Mathematical Programming Interior-Point and Related Methods , Edited by: Megiddo , N. 131 – 158 . New York : Springer-Verlag .
   Google Scholar
• Megiddo , N. , ed. 1989 . Progress in Mathematical Programming-Interior Point and Related Methods , New York : Springer .
   Google Scholar
• Megiddo , N. and Shub , M. 1986 . Boundary Behavior of Interior Point Algorithms in Linear Programming . Math.of O.R , 14 : 97 – 146 .
   Web of Science ®Google Scholar
• Mehrotra , S. 1989 . On Finding a Vertex Solution Using Interior Point Methods , Evanston, IL : Northwestern University . TR89-22R,Department of IE/MS
   Google Scholar
• Mehrotra , S. and Sun , J. 1990 . An algorithm for convex quadratic programming that requires 0(n 3.3 L)A rithmetic Operations . Math.of O.R , 15 : 342 – 363 .
   Web of Science ®Google Scholar
• Miele , A. , Moselly , P.E. , Levy , A.V. and Coggins , G.M. 1972 . On the method of multipliers for mathematical programming problems . J.O.T.A , 10 ( 1 ) : 1 – 33 .
   Google Scholar
• Mifflin , R. 1975 . Convergence bounds for nonlinear programming algorithms . Math.Prog , 8 ( 1 ) : 251 – 271 .
   Web of Science ®Google Scholar
• Mifflin , R. 1976 . Rates of convergence for a method of centers algorithm . J.O.T.A , 18 ( 1 ) : 199 – 228 .
   Web of Science ®Google Scholar
• Mine , H. and Fukushima , M. 1978 . Penalty function theory for general convex programming problems . J.O.T.A , 24 ( 1 ) : 287 – 301 .
   Web of Science ®Google Scholar
• Mitchell , J.E. and Todd , M.J. 1992 . Solving combinatorial optimization problems using Karmarkar's algorithm . Math. Prog , 56 ( 1 ) : 245 – 284 .
   Web of Science ®Google Scholar
• Mizuno , S. 1992 . A new polynomial time method for a linear complementarity problems . Math.Prog , 56 ( 1 ) : 31 – 43 .
   Web of Science ®Google Scholar
• Mizuno , S. and Masuzawa , K. 1989 . Polynomial time interior point algorithms for transportation problems . J.of Oper.Res.Society of Japan , 32 ( 1 ) : 371 – 382 .
   Google Scholar
• Mizuno , S. and Todd , M.J. 1991 . An 0(n 3 L) adaptive path following algorithm for linear complementarity problems . Math.Prog , 52 ( 1 ) : 587 – 595 .
   Web of Science ®Google Scholar
• Monma , C.L. and Morton , A.J. 1987 . Computational experience with a dual affine variant of Karmarkar's method for linear programming . Oper.Res.Letters , 6 ( 1 ) : 261 – 267 .
   Web of Science ®Google Scholar
• Monteiro , R.D.C. 1988 . Convergence and boundary behavior of the projective scaling trajectoriesfor linear programming . In Proc. AMS-IME-SIAM Res. Con$ on Math. Developments Arising from Linear Programming . 1988 . Edited by: Lagarias , J.C. and Todd , M.J. Brunswick, ME : Bowdoin College .
   Google Scholar
• Monteiro , R.D.C. 1992 . On the continuous trajectories for a potential reduction method for linear programming . Math.of O.R , 17 : 225 – 253 .
   Web of Science ®Google Scholar
• Monteiro R. D. C. Adler I. An 0(n 3 L) Primal-Dual Interior Point Algorithm for Convex Quadratic Programming University of California Berkeley 1987 Report ORC 87-4, Operations Research Center, Department of Operations Research
   Google Scholar
• Monteiro , R.D.C. and Adler , I. 1989 . Interior Path-Following Primal-Dual Algorithms, Part I: LP . Math.Prog , 44 : 27 – 41 .
   Web of Science ®Google Scholar
• Monteiro , R.D.C. and Adler , I. 1989 . Interior-Path-Following Primal-Dual Algorithms, Part II Convex Quadratic Programming . Math.Prog , 44 : 42 – 66 .
   Web of Science ®Google Scholar
• Monteiro , R.D.C. and Adler , I. 1990 . An extension of Karmarkar-type algorithm to a class ofconvex separable programming problems with global linear rate of convergence . Math. of O.R , 15 : 408 – 422 .
   Web of Science ®Google Scholar
• Monteiro , R.D.C. , Adler , I. and Resende , M.G.C. 1990 . A polynomial-time primal-dual scaling algorithm for linear and convex quadratic programming and its power series extension . Math. of O.R , 15 : 191 – 214 .
   Web of Science ®Google Scholar
• Moré J. J. Wright S. J. Optimization Software Guide SIAM 1993 Frontiers in Applied Mathematics
   Google Scholar
• Motzkin T. S. New Techniques for Linear Inequalities and Optimization 1952 Project SCOOP Symposium on Linear Inequalities and Programming, Planning Research Division, Director of Management Analysis Service, U.S. Air Force, Washington, DC , No 10
   Google Scholar
• Mouallif , K. and Tossings , P. 1990 . Variational metric and exponential penalization, Technical Note . J.O.T.A , 67 : 185 – 192 .
   Web of Science ®Google Scholar
• Mukai , H. and Polak , E. 1975 . A quadraticaly convergent primal-dual algorithm with global convergence properties for solving optimization problems with equality constraints . Math. Prog , 9 : 336 – 349 .
   Web of Science ®Google Scholar
• Murray , W. Ill-Conditioning in barrier and penalty functions arising in constrained nonlinear programming . paper presented at the Symposium on Mathematical Programming . Princeton.
   Google Scholar
• Murray , W. 1971 . J.O.T.A , 7 : 189 – 196 .
   Google Scholar
• Mylander W. C. Holmes R. L. McCormick G. P. A Guide to SUMT Version 4 1974 RAC-TP-63, Research Analysis Corporation
   Google Scholar
• Nahra , J.E. 1971 . Balance function for the optimal controlproblem . J.O.T.A , 8 : 35 – 48 .
   Google Scholar
• Nesterov Y. E. Nemirovski A. S. Self-concordant Functions and Polynomial Time Methods in Convex Programming 1989 USSR Academy of Sciences, Central Economical and MathematicalInstitute, Report
   Google Scholar
• Nesterov , Y.E. and Nemirovski , A.S. 1971 . Interior-point polynomial algorithms in convex programming . Studies in Applied Mathematics , 13
   Google Scholar
• Newell , J.S. and Himmelbleau , D.M. 1975 . A new method for nonlinear constrained optimization . AICHE J , 21 : 479 – 486 .
   Web of Science ®Google Scholar
• Nguyen , V.H. and Strodiot , J.J. 1979 . On the convergence rate of a penalty function method of exponential type . J.O.T.A , 27 : 873 – 885 .
   Web of Science ®Google Scholar
• O Doherty , R.J. and Pierson , P.L. 1974 . A numerical study of augmented penalty function algorithms for terminally constrained optimal control problems . J.O.T.A , 14 : 393 – 403 .
   Web of Science ®Google Scholar
• O Neill , R.P. and Widhelm , W.B. 1976 . Acceleration of Lagrangian column-generation algorithms by penalty function, Methods . Man. Scien , 23 : 50 – 58 .
   Web of Science ®Google Scholar
• Optima-Routines for Optimization Problems The Hatfield Polytechnic, 19 St. Albans Road,Hatfield, Hertfordshire England
   Google Scholar
• Pappalardo , M. 1990 . J.O.T.A , 64 : 141 – 152 .
   Web of Science ®Google Scholar
• Parisot G. R. Resolution Numerique Approachée du Problem de Programmation Linéaire par Application de la Programmation Logarithmique Universite de Lille Lille, , France 1961 Ph.D. Thesis
   Google Scholar
• Pierre , D.A. 1977 . A robust code for constrained optimization . AIAA J , 5 : 877 – 878 .
   Google Scholar
• Pierre , D.A. and Lowe , M.J. 1975 . Mathematical Programming via Augmented Lagrangian: An Introduction with Computer Programs , Reading, MA : Addison-Wesley .
   Google Scholar
• Pietrzykowski , T. 1962 . Application of the Steepest Descent Method to Concave Programming . Proceedings of the IFIPS Congress . 1962 . pp. 185 – 189 . Amsterdam, , Holland : Munich, North Holland Company .
   Google Scholar
• Pietrzykowski , T. 1969 . An exact potential method for constrained maxima . SIAM J. Numer. Anal , 6 : 269 – 304 .
   Web of Science ®Google Scholar
• Polak , E. 1976 . On theglobal stabilization of locally convergent algorithms . Automatica-J. IFAC , 12 : 337 – 342 .
   Web of Science ®Google Scholar
• Polak , E. and Tits , A.L. 1980 . “ A globally convergent, implementable multiplier method with automatic penalty limitation ” . In Applied Math. and Optim , Vol. 6 , 335 – 360 . Berkeley : Electron. Res. Lab., Univ. of California . Memo No. UCB/ERl M79/52
   Google Scholar
• Poljak , B.T. 1971 . The convergence rate of the penalty method . Z. Vychisl. Mat i Mat. Fiz , 11 : 3 – 11 .
   Google Scholar
• Poljak , B.T. and Tretjakov , N.V. 1974 . An iterative method for linear programming and its economic interpretation . Matecon , 10 : 81 – 100 .
   Google Scholar
• Polyak , R. 1992 . Modified barrier functions(Theory and Methods) . Math. Prog , 54 : 177 – 222 .
   Web of Science ®Google Scholar
• Poore A. B. Al-Hassan Q. The Expanded Lagrangian System for Constrained Optimization Problems Colorado State University CO 1988 Department of Mathematics, 80523
   Google Scholar
• Powell , M.J.D. 1969 . A method for nonlinear constraints in minimization problems, in Optimization , Edited by: Fletcher , R. 283 – 298 . New York : Academic Press .
   Google Scholar
• Powell , M.J.D. 1970 . A survey of numerical methods for unconstrained optimization . SIAM Rev , 12 : 79 – 97 .
   Web of Science ®Google Scholar
• Powell , M.J.D. and Yuan , Y. 1986 . A recursive quadratic programming algorithm that uses differentiable exact penalty functions . Math. Prog , 35 : 265 – 278 .
   Web of Science ®Google Scholar
• Rardin , R.L. and Lin , B.W. 1981 . Test Problems for Computational Experiment-Issues and Techniques, in Lecture Notes in Economics and Mathematical Systems , Edited by: Mulvey , J.M. Vol. 199 , 9 – 15 . Berlin Heidelberg, NY : Springer-Verlag .
   Google Scholar
• Ratner M. W. Fox R. L. CMIN15 Users Guide Cleveland, OH 1975 Ed. 2, CHI Corporation
   Google Scholar
• Renegar , J.A. 1988 . A polynomial-time algorithm based on Newton's Method for linear programming . Math. Prog , 40 : 59 – 93 .
   Web of Science ®Google Scholar
• Rijckaert , M.J. and Martens , X.M. 1978 . Comparison of general geometric programming algorithms . J.O.T.A , 26 : 205 – 248 .
   Web of Science ®Google Scholar
• Robinson , S.M. 1972 . A quadratically convergent algorithm for a general nonlinear programming problems . Math.Prog , 3 : 145 – 156 .
   Google Scholar
• Rockafellar , R.T. 1970 . “ New applications of duality in nonlinear programming ” . In Symposium on Mathematical Programming Hague
   Google Scholar
• Rockafellar , R.T. . New applications of duality in convex programming . Proc.Confer.Probab.,4th . Brasov, Romania. pp. 73 – 81 .
   Google Scholar
• Rockafellar , R.T. 1973 . The multiplier method of Hestenes and Powell applied to convex programming . J.O.T.A , 12 : 555 – 562 .
   Web of Science ®Google Scholar
• Rockafellar , R.T. . Penalty Methods and Augmented Lagrangians in Nonlinear Programming . Lecture Notes in Computer Sciences, 5th Conference on Optimization Techniques, Part I . Edited by: Conti , R. and Ruberti , A. pp. 418 – 425 . New York : Springer-Verlag . Series I.F.I.P. TC7 Optimization Conferences
   Google Scholar
• Roos , C. and Vial , J.P. 1990 . “ Long steps with the logarithmic penalty barrier function ” . In Linear Programming, Economic Decision Making: Games, Economics and Optimization , Edited by: Gabszewicz , J. , Richard , J.F. and Wolsey , L. 433 – 441 . Amsterdam : Elsevier Science Publisher . Holland
   Google Scholar
• Root , R.R. and Ragsdell , K.M. 1980 . Computational enhancements to the method multiplier . ASME J.Mech.Des , 102 ( 3 ) : 517 – 523 .
   Web of Science ®Google Scholar
• Rosen J. B. Two-phase algorithm for nonlinear constraint problems University of Minnesota Minneapolis 1977 Technical Report 77-8,Computer Science Department, , Minn. 55455
   Google Scholar
• Rosenberg , E. 1981 . Globally convergent algorithm for convex programming . Math.of O.R , 6 ( 3 ) : 437 – 444 .
   Web of Science ®Google Scholar
• Rountree , D.T. and Rigler , A.K. 1982 . A penalty treatment of equality constraints in generalized geometric programming . J.O.T.A , 38 ( 3 ) : 169 – 189 .
   Web of Science ®Google Scholar
• Rubin , H. and Ungar , P. 1957 . Motion under a strong constraining force . Communs.Pure Math , 10 ( 3 ) : 65 – 87 .
   Web of Science ®Google Scholar
• Rufer D. User's Guide for NLP-A Subroutine Package to Solve Nonlinear Optimization Problems 1978 Rep. No 78-07, Fachgruppe fur Automatik, Eidgenossisch Technisch Hochschule, Zurich Switzerland
   Google Scholar
• Rupp , R.D. 1972 . Approximation of the classical isoperimetric problem . J.O.T.A , 9 ( 3 ) : 251 – 264 .
   Google Scholar
• Rupp , R.D. 1975 . Convergence and duality for the multiplier and penalty methods . J.O.T.A , 16 ( 3 ) : 99 – 118 .
   Web of Science ®Google Scholar
• Saaty , T.L. 1977 . A scaling method for priorities in hierarchical structures . J.Math.Psych , 15 ( 3 ) : 234 – 281 .
   Web of Science ®Google Scholar
• Sandgren E. The utility of nonlinear programming algorithms 1977 Ph.D. Dissertation, Purdue University, University Microfilm, 300 North Zeeb Road, Ann Arbor, MI, Document No. 7813115
   Google Scholar
• Sandgren , E. and Ragsdell , K.M. 1982 . On some experiments which delimit the utility of nonlinear . Math.Prog.Study , 16 ( 3 ) : 118 – 136 .
   Google Scholar
• Sarma , P.V. , Martens , X.M. , Reklaitis , G.V. and Rijckaert , M.J. 1978 . A comparison of computational strategies for geometric programs . J.O.T.A , 26 ( 3 ) : 185 – 203 .
   Web of Science ®Google Scholar
• Schittkowski , K. 1980 . Nonlinear Optimization Codes , Vol. 183 , Berlin : Springer . Lecture Notes in Economics and Mathematical Systems
   Google Scholar
• Shub , M. 1987 . Asymptotic behavior of the projective rescaling algorithm for linearprogramming . J.of complexity , 3 : 258 – 269 .
   Google Scholar
• Sidall , J.N. 1971 . OPTI-SEP: Designers optimization subroutines , Hamilton, , Canada : McMaster University .
   Google Scholar
• Sonnevend , G. 1985 . An analytical center for polyhedrons and new classes of global algorithms for linear programming . Lecture Notes in Control and Information Science , 84 : 866 – 876 . smooth, convex
   Google Scholar
• Sonnevend , G. A new method for solving a set of linear (convex) inequalities and its applications for identification and optimization . 5th IFAC-IFORS Conf . Budapest. pp. 6 – 8 . Department of Numerical Analysis, Institute of Mathematics
   Google Scholar
• Staha , R.L. 1973 . Documentation for Program COMET , Austin : The University of Texas . A Constrained Optimization Code
   Google Scholar
• Staha R. L. Himmelbleau D. M. Evaluation of of constrained nonlinear programming techniques University of Texas at Austin Texas 1973 Report, Dept. of Chem. Eng., 78712
   Google Scholar
• Tamir , A. 1972 . An efficient algorithm for minimizing barrier and penalty functions . Math. Prog , 3 : 390 – 391 .
   Google Scholar
• Tapia R. A. Zhang Y. A fast optimal basis identification technique for interior point linear programming methods Rice University Houston, Texas 1989 Tech. Rep. No 89-1, Dept, ofMath. Sciences
   Google Scholar
• Tapia , R.A. and Zhang , Y. 1990 . Cubically convergent method for locating a nearby vertex in linear programming . J.O.T.A , 67 : 217 – 235 .
   Web of Science ®Google Scholar
• Todd , M.J. 1988 . Exploiting special structure in Karmarkar’s linear programming algorithm . Math.Prog , 41 : 97 – 113 .
   Web of Science ®Google Scholar
• Todd , M.J. 1988 . Improved bounds and containing ellipsoid in Karmarkar’s linear programming algorithm . Math.of O.R , 13 : 650 – 659 .
   Web of Science ®Google Scholar
• Todd , M.J. 1989 . Recent development and new directions in linear programming, in Mathematical Programming— Recent Developments and Applications , Edited by: Iri , M. and Tanabe , K. 109 – 157 . Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Todd , M.J. and Burrell , B.P. 1986 . An extension of Karmarkar’s algorithm for linear programming . Algorithmica , 1 : 409 – 424 .
   Web of Science ®Google Scholar
• Todd , M.J. and Ye , Y. 1990 . A centered projective algorithm for linear programming . Math. of O.R , 1 : 508 – 529 .
   Web of Science ®Google Scholar
• Tomlin , J.A. 1985 . An Experimental Approach to Karmarkar’s Projective Method for Linear Programming , Mountain View, C.A : Ketron,Inc . Technical Report
   Google Scholar
• Tomlin , J.A. and Welch , J.S. 1986 . Implementing an Interior Point Method in a Mathematical . I, Paper Presented at the ORSAITIMS 22nd Joint National Meeting . 1986 , Miami, Florida.
   Google Scholar
• Tripahni , S.S. and Narendra , K.S. 1972 . Constrained optimization problems using multiplier methods . J.O.T.A , 9 : 59 – 70 .
   Google Scholar
• Tseng , P. 1992 . Global linear convergence of a path-following algorithm for some monotone variational inequality problems . J.O.T.A , 75 : 265 – 279 .
   Web of Science ®Google Scholar
• Tseng , P. and Bertsekas , D.P. 1993 . On the convergence of the exponential multiplier method for . Math. Prog , 60 : 1 – 19 .
   Web of Science ®Google Scholar
• Tsuchiya , T. 1992 . Global convergence property of the affine scaling methods for primal degenerate linear programming problems . Math.of O.R , 17 : 527 – 557 .
   Web of Science ®Google Scholar
• Vaidya , P.M. 1989 . A Locally Well-behaved Potential Function and a Simple Newton-Type Method for Finding the Center of a Polytope, in Progress in Mathematical Programming: Interior Point and Related Methods , Edited by: Megiddo , N. New York : Springer-Verlag .
   Google Scholar
• Vaidya , P.M. 1990 . An algorithm for solving linear programming which requires [ILM0001] arithmetic operations . Math.Prog , 47 : 175 – 201 .
   Web of Science ®Google Scholar
• Vanderbei , R.J. , Meketon , M.S. and Freedman , B.A. 1986 . A modification of Karmarkar’s linear programming algorithm . Algorithmica , 1 : 395 – 407 .
   Web of Science ®Google Scholar
• Van Der Hoek , G. 1982 . Asymptotic properties of reduction methods applying linearly equality constrained reduced problems . Math.Prog.Study , 16 : 162 – 189 .
   Web of Science ®Google Scholar
• Van Der Hoek G. Experiments with a Reduction Method for Nonlinear Programming Based on a Restricted Lagrangian Erasmus University Rotterdam 1978 Report 78041/0, Econometric Institut
   Google Scholar
• Vivante , C. and Pintos , S. 1986 . On differentiable exact penalty functions . J.O.T.A , 50 : 479 – 593 .
   Web of Science ®Google Scholar
• Vlach , M. . Augmented penalty function technique for optimal control problems . Optimization and Operations Research Proceedings . Bonn. Edited by: Henn , R. , Kort , B. and Oettli , W. Lecture Notes in Economics and Mathematical Systems No 157
   Google Scholar
• Volin , Y.M. . Penalty function method and necessary optimum conditions in optimal control problems with bounded state variables . Optimization Techniques, IFIP Technical Conference . Edited by: Goos , G. and Hartmams , J. pp. 128 – 144 . Lecture Notes in Computer Science No. 27
   Google Scholar
• Wallacher , G. and Zimmermann , U. 1992 . A combinatorial interior point method for network flow . Math. Prog , 56 : 321 – 335 .
   Web of Science ®Google Scholar
• Ward , D.E. 1988 . Exact penalties and sufficient conditions for optimality in nonsmooth optimization . J.O.T.A , 57 : 485 – 499 .
   Web of Science ®Google Scholar
• Waren , A.D. , Hung , M.S. and Lasdon , L.S. 1987 . The status of nonlinear programming software:An Updata . Oper.Res , 35 : 489 – 503 .
   Web of Science ®Google Scholar
• Waterman , R.J. 1976 . “ An evaluation and comparison of three nonlinear programming codes ” . In M.S.Thesis , Monterey, CA : Postgraduate School .
   Google Scholar
• Wierzbicki , A.P. 1971 . A penalty function shifting method in constrained static optimization and its convergence properties . Arch.Automat.Telemech , 16 : 395 – 416 .
   Google Scholar
• Witzgall , C. , Boggs , P. and Domich , P. . On the convergence behavior of trajectories for linear . Proc. AMS-IME-SIAM Res. Conf. on Math. Developments Arising from Linear Programming . Brunswick, ME. Edited by: Lagarias , J.C. and Todd , M.J. Bowdoin College .
   Google Scholar
• Wright , M.H. 1992 . Interior methods for constrained optimization , Edited by: Iserles , A. 341 – 407 . New York : Cambridge University Press . Acta Numerica
   Google Scholar
• Yamashita , H. 1986 . A polynomial and quadratically convergent method for linear programming , Tokyo, , Japan : Mathematical System Institute .
   Google Scholar
• Ye , Y. 1987 . Further development on the interior algorithm for convex quadratic programming , Stanford, CA : Stanford University . Manuscript, Department of Engineering-Economics Systems
   Google Scholar
• Ye , Y. 1987 . “ An interior algorithm for linear, quadratic, and linearly constrained convex programming ” . In Ph.D. Dissertation , Stanford, CA : Stanford University . Department of Engineering-Economic Systems
   Google Scholar
• Ye , Y. 1989 . An extension of Karmarkar’s algorithm and the trust region method for quadratic programming , Edited by: Megiddo , N. New York : Springer . Progress in Mathematical Programming
   Google Scholar
• Ye Y. A potential reduction algorithm entropy optimization University of Iowa 1989 College of Business Adminitsration, Report
   Google Scholar
• Ye , Y. 1990 . A ‘Builddown’ scheme for linear programming . Math.Prog , 46 : 61 – 72 .
   Web of Science ®Google Scholar
• Ye , Y. 1990 . Recovering optimal basic variables in Karmarkar’s polynomial algorithm for linear programming . Math.of O.R , 15 : 564 – 572 .
   Web of Science ®Google Scholar
• Ye , Y. 1992 . An affine scaling algorithm for nonconvex quadratic programming . Math.Prog , 56 : 285 – 300 .
   Web of Science ®Google Scholar
• Ye , Y. 1992 . On the finite convergence of interior-point algorithms for linear programming . Math.Prog , 57 : 325 – 335 .
   Web of Science ®Google Scholar
• Ye , Y. and Kojima , M. 1987 . Recovering optimal dual solutions in Karmarkar’s polynomial . Math.Prog , 39 : 305 – 317 .
   Web of Science ®Google Scholar
• Ye , Y. and Potra , F. 1990 . An interior-point algorithm for solving entropy optimization problems with globally linear and locally quadratic convergence rate , University of Iowa . College of Business Adminitsration. Working Paper
   Google Scholar
• Ye , Y. and Todd , M.J. 1990 . Containing and shrinking ellipsoids in the path following algorithm . Math.Prog , 47 : 1 – 9 .
   Web of Science ®Google Scholar
• Ye , Y. and Tse , E. 1989 . An extension of Karmarkar’s projective algorithm for convex quadratic programming . Math.Prog , 44 : 157 – 179 .
   Web of Science ®Google Scholar
• Zangwill , W.I. 1967 . Nonlinear programming via penalty functions . Man.Scien , 13 : 344 – 358 .
   Google Scholar
• Zhu , J. 1992 . A path following algorithm for a class of convex programming problems . Zeitschrift für Operations Research—Methods and Models of Operations Research , 36 : 359 – 377 .
   Google Scholar