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J. Korean Math. Soc. 2006; 43(2): 241-258

Printed March 1, 2006

Copyright © The Korean Mathematical Society.

Invexity as necessary optimality condition in nonsmooth programs

Pham Huu Sach, Do Sang Kim, and Gue Myung Lee

Pukyong National University, Pukyong National University, Pukyong National University

Abstract

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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

MSC numbers: 90C46, 90C26

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