Generalized convexity in non-regular programming problems with inequality-type constraints

作     者：Hernandez-Jimenez, B. Rojas-Medar, M. A. Osuna-Gomez, R. Beato-Moreno, A. 

作者机构：Univ Pablo Olavide Area Estadist & Invest Operat Dept Econ Metodos Cuantitativos & H Econ Seville Spain Univ Seville Dept Estadist & Invest Operat E-41080 Seville Spain Univ Bio Bio Fac Ciencias Dept Ciencias Basicas Casilla 447 Chillan Chile 

出 版 物：《JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS》 (数学分析与应用杂志)

年 卷 期：2009年第352卷第2期

页      面：604-613页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：M.E.C.  (1080628  MTM2007-063432) 

主　　题：Non-regular problem Generalized convexity KKT-invexity Optimality conditions 

摘      要：Convexity plays a very important role in optimization for establishing optimality conditions. Different works have shown that the convexity property can be replaced by a weaker notion, the invexity. In particular, for problems with inequality-type constraints, Martin defined a weaker notion of invexity, the Karush-Kuhn-Tucker-invexity (hereafter KKT-invexity), that is both necessary and sufficient to obtain Karush-Kuhn-Tucker-type optimality conditions. It is well known that for this result to hold the problem has to verify a constraint qualification, i.e., it must be regular or non-degenerate. In non-regular problems, the classical optimality conditions are totally inapplicable. Meaningful results were obtained for problems with inequality-type constraints by lzmailov. They are based on the 2-regularity condition of the constraints at a feasible point. In this work. we generalize Martin s result to non-regular problems by defining an analogous concept, the 2-KKT-invexity, and using the characterization of the tangent cone in the 2-regular case and the necessary optimality condition given by lzMailov. (c) 2008 Elsevier Inc. All rights reserved.