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http://dx.doi.org/10.4134/JKMS.2006.43.2.241

INVEXITY AS NECESSARY OPTIMALITY CONDITION IN NONSMOOTH PROGRAMS  

Sach, Pham-Huu (Institute of Mathematics)
Kim, Do-Sang (Department of Applied Mathematics Pukyong National University)
Lee, Gue-Myung (Department of Applied Mathematics Pukyong National University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.2, 2006 , pp. 241-258 More about this Journal
Abstract
This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.
Keywords
necessary optimality conditions; locally Lipschitz program; invexity; type I invexity; system of sublinear inequalities;
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1 F. H. Clarke, Optimization and nonsmooth analysis, John Wiley & Sons, Inc., New York, 1983
2 B. D. Craven, Nondifferentiable optimization by smooth approximations, Optimization 17 (1986), no. 1,3-17   DOI   ScienceOn
3 M. A. Hanson, Invexity and the Kuhn-Tucker theorem, J. Math. Anal. Appl. 236 (1999), no. 2, 595-604
4 A. Ben-Israel and B. Mond, What is invexity-, J. Austral. Math. Soc. Ser. B 28 (1986), no. 1, 1-9   DOI
5 M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981), no. 2, 545-550   DOI
6 R. T. Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970
7 R. R. Merkovsky and D. E. Ward, General constraint qualifications in nondifferentiable programming, Math. Programming 47 (1990), no. 3, (Ser. A), 389-405   DOI
8 M. A. Hanson and B. Mond, Necessary and sufficient conditions in constrained optimization, Math. Programming 37 (1987), no. 1, 51-58   DOI
9 O. L. Mangasarian, Nonlinear programming, McGraw-Hill, New York, 1969
10 D. H. Martin, The essence of invexity, J. Optim. Theory Appl. 47 (1985), no. 1, 65-76   DOI
11 R. Osuna-Gomez, A. Rufian-Lizana, and P. Ruiz-Canales, Invex functions and generalized convexity in multiobjeetive programming, J. Optim. Theory Appl. 98 (1998), no. 3, 651-66l   DOI   ScienceOn
12 P. H. Sach, G. M. Lee, and D. S. Kim, Infine functions, nonsmooth alternative theorems and vector optimization problems, J. Global Optim. 27 (2003), no. 1, 51-81   DOI
13 T. W. Reiland, Nonsmooth invexity, Bull. Austral. Math. Soc. 42 (1990), no. 3, 437-446   DOI
14 P. H. Sach, G. M. Lee, and D. S. Kim, Efficiency and generalised convexity in vector optimization problems, ANZIAM J. 45 (2004), 523-546   DOI