Scholarlink

<p>In this study, we use weighted directional derivative to introduce the weighted subdifferential for set-valued mappings by means of a nonlinear scalarization function related to weighted set order relations. We obtain several properties of weighted subdifferential for set-valued mappings corresponding to the ones for subdifferential in the sense of convex analysis. The mean value theorem in terms of weighted subdifferential for set-valued mappings is also established. Several examples are provided to illustrate the results of this paper. As applications, we establish necessary and sufficient optimality conditions for a weak minimal solution of the set optimization problems with respect to weighted set order relations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Weighted Subdifferential for Set-valued Mappings with Applications

  • 期刊论文

  • 发表日期：

    2026年5月5日

查看全文
  • Qamrul Hasan Ansari,
  • Mohd Lukman

摘要

In this study, we use weighted directional derivative to introduce the weighted subdifferential for set-valued mappings by means of a nonlinear scalarization function related to weighted set order relations. We obtain several properties of weighted subdifferential for set-valued mappings corresponding to the ones for subdifferential in the sense of convex analysis. The mean value theorem in terms of weighted subdifferential for set-valued mappings is also established. Several examples are provided to illustrate the results of this paper. As applications, we establish necessary and sufficient optimality conditions for a weak minimal solution of the set optimization problems with respect to weighted set order relations.