General lagrange-type functions in constrained global optimization part II: Exact auxiliary functions

References

• Andramonov , M.Yu. 2000 . “ An approach to constructing generalized penalty function ” . In Optimization and related topics , Edited by: Rubinov , A.M. and Glover , B. M. 3 – 14 . Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Bazaraa , M.S. and Goode , J.J. 1982 . Sufficient conditions for a globally exact penalty function without convexity . Mathematical Programming Study , : 1 – 15 .
   Google Scholar
• Bertsecas , D.P. 1982 . Constrained Optimization and Lagrange Multiplier Methods , New-York : Academic Press .
   Google Scholar
• Burke , J. 1991 . An exact penalization viewpoint of constrained optimization . SIAM J. Control and Optimization , 29 : 968 – 998 .
   Web of Science ®Google Scholar
• Charalambous , Ch. 1976 . A negative-positive Barrier method for non-linear programming . Internat. J. Systems Sci. , 7 : 557 – 575 .
   Web of Science ®Google Scholar
• Demyanov , V.F. , Di Pillo , G. and Facchinei , F. 1998 . Exact penalization via Dini and Hadamard conditional derivatives . Optimization Methods and Software , 9 : 19 – 36 .
   Web of Science ®Google Scholar
• Dolecky , S. and Rolewich , S. 1979 . Exact penalties for local minima . SZAM J. Control and Optimization , 17 : 596 – 606 .
   Google Scholar
• Eremin , LI. 1967 . “ The "penalty" method in convex programming ” . In Dokl. Akad. , Vol. 173 , 748 – 751 . Russian : Nauk SSSR .
   Google Scholar
• Evtushenko , Yu.G. 1987 . “ Accuracy estimation for penalty function methods ” . In Problems of Applied Mathematics and Computer Science , 199 – 208 . Moscow, Russian : Nauka .
   Google Scholar
• Evtushenko , Y.G. and Zhadan , V.G. 1990 . Exact auxiliary functions in optirnization problems . U.S.S.R. Comput. Maths. Math. Phys. , 30 : 31 – 42 .
   Google Scholar
• Evtushenko , Y.G. and Zhadan , V.G. 1990 . Exact auxiliary functions . Informatica , 1 : 40 – 58 .
   Google Scholar
• Evtushenko , Y.G. and Zhadan , V.G. 1992 . “ Exact auxiliary functions in non-convex optimization ” . Edited by: Oettli , W. and Pallaschke , D. 217 – 226 . Berlin : Springer-Verlag . (Lecture Notes in Economics and Mathematical Systems, 382)
   Google Scholar
• Evtushenko , Y.G. , Rubinov , A.M. and Zhadan , V.G. 2001 . General Lagrange-type functions in constrained global optimization . Part I: Auxiliary functions and Optimality Conditions, Optimization Methods and Software , 16 : 179 – 217 .
   Google Scholar
• Han , S.P. and Mangasarian , O.L. 1979 . Exact penalty functions in nonlinear programming . Mathematical Programming , 17 : 251 – 269 .
   Web of Science ®Google Scholar
• Huard P. Resolution des P.M. a constraintes non-lineaires par la methode des centres 1964 17
   Google Scholar
• Kowalik , J. , Osborn , M.R. and Ryan , D.M. 1969 . A new method for constrained optimization problems . Operat. Res.: , 17 : 973 – 989 .
   Web of Science ®Google Scholar
• Morrison , D.D. 1968 . Optimization by least squares . SZAM J. Numer. Analysis , 5 : 83 – 88 .
   Web of Science ®Google Scholar
• Di Pillo , G. and Grippo , L. 1989 . Exact penalty functions in constrained optimization . SZAM J. Control Optim. , 27 : 1333 – 1360 .
   Web of Science ®Google Scholar
• Pollaschke D. Roleviwics S. Foundations of Mathematical Optimization Kluwer Academic Publishers. 1997
   Google Scholar
• Rubinov , A. M. 2000 . Abstract Convexity and Global Optimization , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Rubinov , A.M. , Glover , B.M. and Yang , X.Q. 1999 . Extentled Lagrange and penalty functions in continuous optimization . Optimization , 46 : 327 – 351 .
   Google Scholar
• Rubinov , A.M. , Glover , B.M. and Yang , X.Q. 2000 . Decreasing functions with application to penalization . SIAM Journal Optimization , 10 : 289 – 313 .
   Web of Science ®Google Scholar
• Rubinov , A. M. and Uderzo , A. 2000 . On global optimality condtions via separation functions . Journal of Optimization Theory and Applications , 10 to appear
   Google Scholar
• Singer I. Abstract Convex Analysis Wiley and Sons 1997
   Google Scholar
• Velichenko , V.V. 1967 . A method for determining the constrained minimum of a function of many variables , Vol. 2 , 171 – 172 . Russian : Antomatika i telemechan .
   Google Scholar
• Yang , X.Q. and Teo , K.L. 1967 . Nonlinear Lagrangian functions and applications to semi-infinite programs, optimization and numerical algebra . Annals of Operations Research , 2 to appear
   Google Scholar
• Zangwill , W. 1967 . Nonlinear programming via penalty function . Management Sciences , 13 : 344 – 358 .
   Google Scholar
• Zhadan , V.G. 1984 . On some estimations of penalty coefficient in methods of exact penalty functions . U.S.S.R. Comput. Maths. Math. Phys. , 24 : 124 – 128 .
   Google Scholar