Second-order optimality conditions with the envelope-like effect for nonsmooth vector optimization in infinite dimensions

被引：9

作者：

Phan Quoc Khanh ^{[1
]}

Nguyen Dinh Tuan ^{[2
]}

机构：

[1] Int Univ Hochiminh City, Dept Math, Ho Chi Minh City, Vietnam

[2] Univ Econ Hochiminh City, Dept Math & Stat, Ho Chi Minh City, Vietnam

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 77卷

关键词：

Nonsmooth vector optimization; Second-order optimality conditions; Envelope-like effect; Weak solutions; Firm solutions; First and second-order approximations; Asymptotic p-compactness; (strict) differentiability; MULTIOBJECTIVE OPTIMIZATION; INEQUALITY CONSTRAINTS; MINIMIZATION PROBLEMS; METRIC REGULARITY; BANACH-SPACES; TANGENT SETS; APPROXIMATIONS; DERIVATIVES; 1ST-ORDER; MAPPINGS;

D O I：

10.1016/j.na.2012.09.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Second-order necessary conditions and sufficient conditions with the envelope-like effect for optimality in nonsmooth vector optimization are established. We use approximations as generalized derivatives, imposing strict differentiability for necessary conditions and differentiability for sufficient conditions and avoiding continuous differentiability. Convexity conditions are not imposed explicitly. The results make it clear when the envelope-like effect occurs and improve or include several recent existing ones. Examples are provided to show advantages of our theorems over some known ones in the literature. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：130 / 148

页数：19

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