Second-Order Optimality Conditions for Strict Pareto Minima and Weak Efficiency for Nonsmooth Constrained Vector Equilibrium Problems

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2022-10-17 DOI:10.1080/01630563.2022.2132510

T. Su, D. Luu

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引用次数: 0

Abstract

Abstract In this article, some types of lower and upper second-order strictly pseudoconvexity are provided for establishing sufficient conditions for the second-order strict local Pareto minima of nonsmooth vector equilibrium problem with set, inequality and equality constraints. Based on the notion of Gerstewitz mappings, some Kuhn-Tucker-type multiplier rules for the strict local Pareto minima of such problem are obtained. We also construct the second-order constraint qualification in terms of first- and second-order directional derivatives of the (CQ) and (CQ1) types. Using this constraint qualifications, some second-order primal and dual necessary optimality conditions in terms of second-order upper and lower Dini directional derivatives for such minima are derived. Under suitable assumptions on the lower and upper strictly pseudoconvexity of order two of objective and constraint functions, second-order necessary optimality conditions become sufficient optimality conditions to such problem. Some illustrative examples are also given for our findings.

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严格Pareto极小的二阶最优性条件和非光滑约束向量平衡问题的弱有效性

摘要本文给出了具有集合、不等式和等式约束的非光滑向量平衡问题的二阶严格局部Pareto极小的充分条件，给出了一些类型的上、下二阶严格伪凸性。基于Gerstewitz映射的概念，得到了这类问题的严格局部Pareto极小的Kuhn-Tucker型乘子规则。我们还根据（CQ）和（CQ1）类型的一阶和二阶方向导数构造了二阶约束条件。利用这一约束条件，导出了这类极小值的二阶上下Dini方向导数的一些二阶原最优性和对偶最优性必要条件。在对目标函数和约束函数的二阶严格伪凸性的适当假设下，二阶必要最优性条件成为该问题的充分最优性条件。文中还举例说明了我们的发现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.