General lagrange-type functions in constrained global optimization Part I: auxiliary functions and optimality conditions

References

• Andramonov , M. and 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 . Kluwer Academic Publishers .
   Google Scholar
• Aubin , J.-P. and Ekeland , I. 1984 . Applied Nonlinear Analysis , New York : John Wiley and Sons .
   Google Scholar
• Burke , J. 1991 . An exact penalization viewpoint of constrained optimization . SZAM J. Control and Optimization , 29 : 968 – 998 .
   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 Sofiware , 9 : 19 – 36 .
   Web of Science ®Google Scholar
• Dixon , L.C. and Szego , G.P. 1975, 1978 . Towards Global Optimization , Amsterdam : North Holland . (part I , part 11)
   Google Scholar
• Eremin , I. I. 1967 . “ The "penalty" method in convex programming ” . In Dokl. Akad , Vol. 173 , 748 – 751 . Russian : Nauk SSSR .
   Google Scholar
• Evtushenko , Y.G. and Zhadan , V.G. 1990 . Exact auxiliary functions in optimization problems . U.S.S.R. Comput. Marilr. Math. Pizys. , 30 : 31 – 42 .
   Google Scholar
• Evtushenko , Y.G. and Zhadan , V.G. 1990 . Exact auxiliary functions . Znformatica , 1 : 40 – 58 .
   Google Scholar
• Evtushenko , Y.G. and Zhadan , V.G. 1992 . “ Exact auxiliary functions in non-convex optimization ” . In Advances in Optimization , 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. 1992 . General Lagrangetype functions in constrained global optimization . Part II: Exact Auxiliary functions, Optimization Methods and Software ,
   Google Scholar
• Giannessi , F. 1984 . Theorems of alternative and optimality conditions . J.Optimization Theory and Applications , 42 : 331 – 365 .
   Web of Science ®Google Scholar
• Giannessi , F. 1994 . “ General optimality conditions via a separation scheme ” . In Algorithms for Continuous Optimization , Edited by: Spedicato , E. 1 – 23 . Kluwer Academi Publisher .
   Google Scholar
• Goh , C.J. and Yang , X.Q. 2001 . A Nonlinear Lagrangian theory for non-convex optimization . Journal of Optimization Theory and Applications , 109 : 99 – 121 .
   Web of Science ®Google Scholar
• Han , S.P. and Mangasanan , O.L. 1979 . Exact penalty functions in nonlinear programming . Mathematical Programming , 17 : 251 – 269 .
   Web of Science ®Google Scholar
• Di Pillo , G. and Grippo , L. 1979 . A new class of augmented Lagrangian in nonlinear programming . SIAM J.Conrrol Optim. , 17 : 618 – 628 .
   Web of Science ®Google Scholar
• Di Pillo , G. and Grippo , L. 1989 . Exact penalty functions in constrained optimization . SIAM J. Control Optim. , 27 : 1333 – 1360 .
   Web of Science ®Google Scholar
• Rockafellar , R.T. and Wets , R.J-B. 1998 . Variational Analysis , Berlin-Heidelberg : Springer Verlag .
   Google Scholar
• Rubinov , A.M. 2000 . Abstract Convexity and Global Optimization , Kluwer Academic Publishers .
   Google Scholar
• Rubinov , A.M. , Glover , B.M. and Yang , X.Q. 1999 . Extended 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 conditions via separation functions . Journal of Optimization Theory and Applications , 10 to appear
   Google Scholar
• Yang , X.Q. and Teo , K.L. 2000 . Nonlinear Lagrangian functions and applications to semi-infinite programs . Optimization and numerical algebra. Annals of Operations Research , 10 to appear
   Google Scholar
• Zangwill , W. 1967 . Nonlinear programming via penalty function . Management Sciences , 13 : 344 – 358 .
   Google Scholar