A generalized karush-kuhn-tucki optimality condition without constraint qualification using tl approximate subdifferential

References

• Ben-Tal , A. and Zlobec , S. 1976 . Characterization of optimality in convex programming without a constraint qualification . Journal of Optimization Theory and Applications , 20 : 417 – 437 .
   Google Scholar
• Borwein , J.M. 1982 . Continuity and differentiability properties of convex operators . Pro-ceedings of the London Mathematical Society , 44 ( 3 ) : 420 – 444 .
   Web of Science ®Google Scholar
• Borwein , J.M. and Wolkowicz , H. 1982 . Characterization of optimality without constraint qualification for the abstract convex program . Mathematical Programming Study , 19 ( 3 ) : 77 – 100 .
   Google Scholar
• Clarke , F.H. 1983 . Optimization and nonsmooth analysis , New York : Wiley-Interscience .
   Google Scholar
• Craven , B.D. 1978 . Mathematical programming and control theory , London : Chapman-Hall .
   Google Scholar
• Craven , B.D. and Zlobec , S. 1980 . Complete characterization of optimality for convex programming in Banach spaces . Applicable Analysis , 11 : 61 – 78 .
   Google Scholar
• Craven , B.D. , Glover , B.M. and Zlobec , S. 1983 . On minimization subject to cone-constraints . Numerical Functional Analysis and Optimization , 6 : 363 – 378 .
   Web of Science ®Google Scholar
• Dien , P.H. 1985 . On the regularity condition for the extremal problem under locally Lipschitz inclusion constraints . Applied Mathematics and Optimization , 13 : 151 – 161 .
   Google Scholar
• Diestel , J. 1984 . “ Graduate Texts in Mathematics ” . In Sequences and series in Banach spaces , Vol. 92 , New York : Springer-Verlag .
   Google Scholar
• Diestel , J. 1975 . “ Lecture Notes in Mathematics ” . In Geometry of Banach spaces—selected topics , Vol. 485 , New York : Springer-Verlag .
   Google Scholar
• Dudley , R.M. 1989 . Real analysis and probability , Pacific Grove, , California : Wadsworth & Brooks .
   Google Scholar
• Ekeland , L. 1974 . On the variational principle . Journal of Mathematical Analysis and Applications , 47 : 324 – 353 .
   Web of Science ®Google Scholar
• Flam , S. 1992 . Lagrangian conditions and stochastic programming . SIAM Journal of Control and Optimization , 30 : 1 – 10 .
   Google Scholar
• Ellaia , R. and Hassouni , A. 1991 . Characterization of nonsmooth functions through their generalized gradients . Optimization , 22 ( 3 ) : 401 – 416 .
   Google Scholar
• Giles , J.R. and Sciffer , S. 1992 . “ Locally Lipschitz functions are generically pseudoregular on separable Banach spaces ” . In Bulletin of the Australian Mathematical Society , Department of Mathematics,University of Newcastle . to appear,Preprint
   Google Scholar
• Glover , B.M. 1984 . Generalized convexity in nondifferentiable programming . Bulletin of the Australian Mathematical Society , 30 ( 2 ) : 193 – 218 .
   Web of Science ®Google Scholar
• Glover , B.M. 1992 . Locally compactly Lipschitzian mappings in infinite dimensional programming . Bulletin of the Australian Mathematical Society , 30 ( 2 ) to appear
   Google Scholar
• Glover , B.M. and Craven , B.D. 1992 . A Fritz John optimality condition using the approximate subdifferential , Vol. 2 , Department of Mathematics,University of Melbourne . submitted for publication, Preprint
   Google Scholar
• Hiriart-Urruty , J.B. 1986 . Generalized differentiability, duality and optimization for problems dealing with differences of convex functions , Vol. 256 , 37 – 70 . Berlin : Springer-Verlag .
   Google Scholar
• Horst , R. 1986 . A general class of branch and bound methods in global optimization with some new approaches for concave minimization . Journal of Optimization Theory and Applications , 51 : 271 – 291 .
   Web of Science ®Google Scholar
• Horst , R. , Phong , T.Q. , Thoai , Ng.V. and Vries , J. de . 1986 . On solving a D. C. programming problem by a sequence of linear programs . Journal of Global Optimization , 1 : 183 – 203 .
   Google Scholar
• Horst , R. and Tuy , N.V. 1990 . Global optimization: Deterministic approaches , Berlin : Springer .
   Google Scholar
• Ioffe , A.D. 1984 . Approximate subdifferentials and applications I: The finite dimensiona theory . Transactions of the American Mathematical Society , 281 : 389 – 416 .
   Web of Science ®Google Scholar
• Ioffe , A.D. 1986 . Approximate subdifferentials and applications II: Functions on locally convex spaces . Mathematika , 33 : 111 – 128 .
   Google Scholar
• Ioffe , A.D. 1989 . Approximate subdifferentials and applications III: The metric theory . Mathematika , 33 : 1 – 38 .
   Google Scholar
• Jourani , A. and Thibault , L. 1990 . Approximate subdifferential and metric regularity: the finite dimensional case . Mathematical Programming , 47 : 203 – 218 .
   Web of Science ®Google Scholar
• Jourani , A. and Thibault , L. 1990 . The use of metric graphical regularity in approximate subdifferential calculus rules in finite dimensions . Optimization , 21 : 509 – 519 .
   Google Scholar
• Jourani , A. and Thibault , L. 1992 . Approximation and metric regularity in mathematical programming in Banach spaces . Mathematics of Operations Research , 21 to appear
   Google Scholar
• Jourani , A. and Thibault , L. 1992 . Approximate subdifferential of composite functions . Bulletin of the Australian Mathematical Society , 21 to appear
   Google Scholar
• 1969 . Nonlinear programming McGraw-Hill, New York
   Google Scholar
• Mordukhovich , B.S. 1984 . Nonsmooth analysis with nonconvex generalized differentials an dual maps . Dokl. Akad. Nauk. BSSR , 28 : 976 – 979 .
   Google Scholar
• Parthasarathy , K.R. 1967 . Probability measures on metric spaces , NewYork : Academic Press .
   Google Scholar
• Poliquin , R. and Qi , L. 1992 . Subderivatives and iterative schemes in nonsmooth optimi-zation | , University of New South Wales . Applied Mathematics Preprint AM92/2, School Mathematical Society
   Google Scholar
• Ribarska , N. 1992 . Proceedings of the American Mathematical Society . The dual of a Gateaux smooth Banach space is weak^∗ fragment able , to appear
   Google Scholar
• Rockafellar , R.T. 1974 . “ Larange multipliers for an N-stage odel in stochastic convex programming, Lecture Notes in Economics and Mathematical Systems ” . In Analyse Convexe et ses applications , Edited by: Aubin , J.P. Vol. 120 , 180 – 187 . Berlin : Springer-Verlag .
   Google Scholar
• Rockafellar , R.T and Wets , R.J.B. 1974 . Continuous versus measurable recourse in N-stage stochastic programming . Journal of Mathematical Analysis and Applications , 48 : 836 – 859 .
   Google Scholar
• Rockafellar , R.T. and Wets , R.J.B. 1977 . Measures as Lagrange multipliers in multi-stage stochastic programming . Journal of Mathematical Analysis and Applications , 60 : 301 – 313 .
   Web of Science ®Google Scholar
• Thibault , L. 1978 . “ Subdifferentials of compactly Lipschitzian vector-valued functions ” . In vaux du Seminaire d'analyse convexe , Montpellier : Fascicule I .
   Google Scholar
• Thibault , L. 1982 . Subdifferentials of nonconvex vector-valued functions . Journal of Math-ematical Analysis and Applications , 86 : 319 – 354 .
   Web of Science ®Google Scholar
• Thibault , L. 1992 . “ Optimization and nonsmooth analysis ” . In Lagrange-Kuhn-Tucker multipliers for general mathematical programming problems , Edited by: Ioffe , A. 311 – 315 . Longman .
   Google Scholar
• Treiman , J.S. 1986 . Clarke's gradients and epsilon-subgradients in Banach spaces . Trans-actions of the American Mathematical Society , 294 : 65 – 78 .
   Google Scholar
• Zlobec , S. and Jacobson , D.H. 1980 . Minimizing an arbitrary function subject to convex constraints . Utilitas Mathematica , 17 : 239 – 257 .
   Google Scholar