Optimality Conditions for Approximate Solutions of Set Optimization Problems with the Minkowski Difference

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-10-23 DOI:10.3390/axioms12101001

Yuhe Zhang, Qilin Wang

引用次数: 0

Abstract

In this paper, we study the optimality conditions for set optimization problems with set criterion. Firstly, we establish a few important properties of the Minkowski difference for sets. Then, we introduce the generalized second-order lower radial epiderivative for a set-valued maps by Minkowski difference, and discuss some of its properties. Finally, by virtue of the generalized second-order lower radial epiderivatives and the generalized second-order radial epiderivatives, we establish the necessary optimality conditions and sufficient optimality conditions of approximate Benson proper efficient solutions and approximate weakly minimal solutions of unconstrained set optimization problems without convexity conditions, respectively. Some examples are provided to illustrate the main results obtained.

查看原文本刊更多论文

具有Minkowski差分的集优化问题近似解的最优性条件

本文研究了具有集准则的集优化问题的最优性条件。首先，我们建立了集的闵可夫斯基差分的几个重要性质。然后，利用Minkowski差分引入集值映射的广义二阶下径向表皮，并讨论了它的一些性质。最后，利用广义二阶下径向表皮子和广义二阶径向表皮子，分别建立了无凸条件下无约束集优化问题近似Benson固有有效解和近似弱极小解的必要最优性条件和充分最优性条件。给出了一些例子来说明所得到的主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.