25
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

COMPUTATIONAL ASPECTS OF GEOMETRIC PROGRAMMING 2. POLYNOMIAL PROGRAMMING

Pages 121-145 | Published online: 27 Feb 2007

REFERENCES

  • R. J. Duffin , E. L. Peterson and C. Zener , Geometric Programming—Theory and Application , John Wiley , N.Y. ( 1967 ).
  • D. J. Wilde and C. S. Beightler , Foundations of Optimization , Prentice-Hall . N.J. ( 1967 ).
  • R. Dembo , M. Avriel and U. Passy , “ An algorithm for the solution of generalized geometiric programs ,” J., Num. Methods in Eng. 2 , 149 – l68 ( 1975 |y)
  • A. R. Colville “ A comparative study of nonlinear programming codes .” IBM Scientific Centre Report No. 320-2949 N.Y. ( 1968 ).
  • D. M. Himmelblau , Applied Nonlinear Programming , McGraw-Hill . N.Y. ( 1972 ).
  • J. Asaadi , “ A computational comparison of some nonlinear programs ,” Math. Prog. . 4 , 144 – 154 ( 1973 ).
  • M. Avriel and A. C. Williams , “ Complementary geometric programming ,” SIAM J. Appl. Math. 19 . 125 – 141 ( 1970 ).
  • R. J. Duffin and E. L. Peterson , “ Geometric programming with signomials .” J. Opt. Theory and Applies . 11 , 3 – 35 (1973).
  • R. J. Duffin and E. L. Peterson , “ Reversed geometric programs treated by harmonic means ,” Research Report , No. 71 – 19 , Carnegie-Mellon University ( 1971 ) ( to appear, Indiana Univ. Math. Jour. ).
  • M. Hall “ Some problems of civil engineering analysis and the theory of (generalized) geometric programming ,” Eng. Opt. 2 ( 2 ), 111 – 123 ( 1976 ).
  • J. Bradley , “ The development of polynomial programming algorithms with applications ,” unpublished Ph.D. Thesis , Trinity College , Dublin ( 1975 ).
  • R. S. Staha and D.M. Himmelblau , “ An evaluation of nonlinear programming techniques for problems with nonlinear constraints ,” presented at Symp. on NLP , George Washington University ( March 1973 ).
  • A. V. Fiacco and G. P. McCormick , Nonlinear Programming—Sequential Unconstrained Minimization Techniques , John Wiley , N. Y. ( 1968 ).
  • M. C. Biggs , “ Computational experience with Murray's method for constrained minimization ,” N.O.C. Research Report. No. 23 ( 1971 ).
  • W. Murray “ An algorithm for constrained minimization ,” in Optimization (ed. R. Fletcher ), Academic Press , London ( 1969 ).
  • M. C. Biggs , “ Constrained minimization using recursive equality quadratic programming ,” in Numerical Methods for Nonlinear Optimization (ed. F. Looisma ), Academic Press , London ( 1972 ).
  • G. P. McCormick , “ Penalty function versus non-penalty function methods for contrained nonlinear programming problems ,” Math. Prog. 1 , 217 – 238 ( 1971 ).
  • J. E. Kelly , “ The cutting plane method for solving convex programmes ,” SIAM J. Appl. Math. 8 , 703 – 712 ( 1960 ).
  • H. O. Hartley and R. R. Hocking , “ Convex programming by tangential approximation ,” Man. Sci. 9 , 600 – 612 ( 1963 ).
  • R. J. Duffin , “ Linearizing geometric programs ,” SIAM Rev. 12 . 211 – 227 ( 1970 ).
  • W. Gochet and Y. Smeers , “ On the use of linear programs to solve prototype geometric programs ,” CORE Report, No. 7229 . Louvain ( 1972 ).
  • P. Wolfe “ Convergence theory in nonlinear programming ,” in Integer and Nonlinear Programming (ed. J. Abadie ), North-Holland , Amsterdam ( 1970 ).
  • G. S. Dawkins , B. C. Mcinnis and S. K. Moonat , “ Solution to geometric programming problems by transformation to convex programming problems ,” Int. J. Solids Structures 10 , 135 – 136 ( 1974 ).
  • J. G. Ecker and M. J. Zoracki , “ An easy primal method for geometric programming ,” Research Report , Rensselaer Polytechnic N.Y. ( 1974 ).
  • R. J. Duffin and E. L. Peterson , “ The proximity of (algebraic) geometric programming to linear programming .” Math. Prog. 3 , 250 – 253 ( 1972 ).
  • J. K. Sengupta , Stochastic Programming , North-Holland , Amsterdam ( 1972 ).
  • R. Dembo , “ Survey of the relative efficiency of computer codes for the solution of geometric programming problems ,” to appear .
  • G. A. Kochenberger . R. E. D. Woolsey and B. A. McCarl , “ On the solution of geometric programs via separable programming ,” Opl. Res. Q. 24 , 285 – 296 ( 1973 ).
  • A. B. Templeman , “ On the solution of geometric programs via separable programming ,” Opl. Res. Q. 25 , 184 ( 1974 ).
  • A. B. Templeman , A. J. Wilson and S. K. Winterbottom , “ SIGNOPT—a computer code for solving geometric programming problems ,” Research Report. Dept. of Civil Engineering . University of Liverpool ( 1972 ).
  • J. Folkers , “ Ship operation and design ,” in Optimization and Design (ed. Avriel , Rijckaert and Wilde ), Prentice-Hall , N.J. ( 1973 ).
  • G. W. Westley , “ A geometric programming algorithm ,” Oak Ridge National Laboratory, Technical Report No. ORNL-4650 ( 1971 ).
  • A. J. Morris , “ The optimization of statically indeterminate structures by means of approximate geometric programming .” Proc. 2nd AGARD Symp. on Structural Optimization , AGARD-CP-123-1973 .
  • B. A. Murtagh and R. W. H. Sargent , “ A constrained minimization method with quadratic convergence ,” in Optimization (ed. R. Fletcher ), Academic Press , London , pp. 215 – 246 ( 1969 ).
  • R. Fletcher and S. A. Lill , “ A class of methods for nonlinear programming—Part II: Computational experience .” in Nonlinear Programming (ed. et al. ,), Academic Press , N.Y. ( 1970 ).
  • P. A. Beck and J. G. Ecker , “ A modified concave simplex algorithm for geometric programming ,” O.R. and Statistics Research Paper, No. 27-72-P6 , Rensselaer Polytechnic Institute , New York ( 1972 ).
  • W. I. Zangwill , Nonlinear Programming—A Unified Approach , Prentice-Hall , N.J. ( 1969 ).
  • P. E. Gill and W. Murray , Numerical Methods for Constrained Optimization , Academic Press , London ( 1974 ).
  • T. Jefferson , “ Geometric programming, with an application to transportation planning ,” Ph.D. thesis , Northwestern University ( 1972 ).
  • J. J. Dinkel , G. A. Kochenberger and B. McCarl , “ An approach to the numerical solutions of geometric programmers ,” Math. Prog. 7 , 181 – 190 ( 1974 ).
  • J. Bradley , “ NEWTGP—An algorithm for the numerical solution of prototype geometric programs ,” Report, Dept. of Computer Science , Trinity College , Dublin ( 1973 ).
  • E. Polak , Computational Methods in Optimization , Academic Press , N.Y. ( 1971 ).
  • P. Wolfe , “ On the convergence of gradient methods under constraint ,” IBM J. Res. Dev. , July , 407 – 411 ( 1972 ).
  • R. Fletcher , “ An algorithm for solving linearly constrained optimization problems ,” Math. Prog. 2 , 133 – 165 ( 1972 ).
  • D. H. Ballard , C. O. Jelinek and R. Schinzinger , “An algorithm for the solution of constrained polynomial programming problems,” Comp. J. (U.K.) 17. 261–266 (1974).
  • G. E. Blau and D. J. Wilde , “ A Lagrangian algorithm for equality constrained generalized polynomial optimization .” AICHE . 17 , 235 – 240 ( 1971 ).
  • M. J. Rijckaert , “ Engineering applications of geometric programming ,” in Optimization and Design (ed. Avriel , Rijckaert and Wilde ). Prentice-Hall , N.J. , pp. 193 – 220 ( 1973 ).
  • D. T. Phillips “ Geometric programming wild slack constraints and degrees of difficulty ,” AIEE Trans . March , 7 – 13 ( 1973 ).
  • R. Hooke and T. A. Jeeves . “ Direct search solution of numerical and statistical problems .” J. ACM 8 , 212 – 219 (1961).
  • C. J. Frank . “ An algorithm for geometric programming ,” in Recent Advances in Optimization Techniques (ed. Lavi and Vogl ). John Wiley . N.Y. , pp. 145 – 162 ( 1966 ).
  • R. J. DulTin and E. L. Peterson , “ Geometric programs treated with slack variables ,” Appl. Analysis 2 , 255 – 267 ( 1972 ).
  • G. P. McCormick , “ Anti-zigzagging by bending ,” Man. Sci. 15 , 315 – 320 ( 1969 ).
  • C. S. Beightler and D. T. Phillips , Applied Geometric Programming , John Wiley , N.Y. ( 1976 ),

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.