On the functions with pseudoconvex sublevel sets and optimality conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:345

Article

Ivanov, Vsevolod I.

关键词: nonsmooth analysis;    nonsmooth optimization;    generalized convex functions;    optimality conditions;    lower hadamard directional derivative;   

DOI  :  10.1016/j.jmaa.2008.05.010

来源: Elsevier

【 摘 要 】

A new class of generalized convex functions, called the functions with pseucloconvex sublevel sets, is defined. They include quasiconvex ones. A complete characterization of these functions is derived. Further, it is shown that a continuous function admits pseudoconvex sublevel sets if and only if it is quasiconvex. Optimality conditions for a minimum of the nonsmooth nonlinear programming problem with inequality, equality and a set constraints are obtained in terms of the lower Hadamard directional derivative. In particular sufficient conditions for a strict global minimum are given where the functions have pseudoconvex sublevel sets. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free