Optimality Conditions for Multiobjective Optimization Problems via Image Space Analysis

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2023-05-12 DOI:10.1080/01630563.2023.2208867

Yingrang Xu, S. Li

引用次数: 0

Abstract

Abstract In this article, optimality conditions on (weak) efficient solutions in multiobjective optimization problems are investigated by using the image space analysis. A class of strong separation functions is constructed by oriented distance functions. Simultaneously, a generalized Lagrange function is introduced by the class of strong separation functions. Then, generalized Karush-Kuhn-Tucker (KKT for short) necessary optimality conditions are established without constraint qualifications or regularity conditions. Under the suitable assumptions, Lagrangian-type sufficient optimality conditions are also characterized. Moreover, the difference between strong separation and weak separation methods is explained.

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基于图像空间分析的多目标优化问题最优性条件

摘要利用图像空间分析方法，研究了多目标优化问题(弱)有效解的最优性条件。用有向距离函数构造了一类强分离函数。同时，通过强分离函数类引入了广义拉格朗日函数。然后，建立了广义Karush-Kuhn-Tucker(简称KKT)必要最优性条件，不考虑约束条件和正则性条件。在适当的假设下，还刻画了拉格朗日型充分最优性条件。并对强分离和弱分离方法的区别进行了说明。

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.