Scholarlink

<p>Based on subdifferentials and conjugate functions, we obtain conjugate duality theorems of set optimization problem under set-order relations. This paper has two main purposes. One is to put forward a new notion of subdifferential of set-valued maps based on <i>m</i>-order relations, and establish some properties of the subdifferential, such as convexity, closedness and homogeneity. The other is to propose new conjugate and biconjugate maps of set-valued maps via the Minkowski difference, obtain some relations among the maps and the subdifferential, and establish optimality conditions, weak and strong conjugate duality theorems of set-order solutions to set optimization problem. Finally, we apply the main results of the paper to uncertain optimization problems. communicated by Tuyen Van Nguyen.</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

Conjugate duality in set optimization via subdifferential respect to set-order relations

  • 期刊论文

  • 发表日期：

    2026年5月19日

查看全文
  • Yuwen Zhai,
  • Guolin Yu,
  • Tian Tang

摘要

Based on subdifferentials and conjugate functions, we obtain conjugate duality theorems of set optimization problem under set-order relations. This paper has two main purposes. One is to put forward a new notion of subdifferential of set-valued maps based on m-order relations, and establish some properties of the subdifferential, such as convexity, closedness and homogeneity. The other is to propose new conjugate and biconjugate maps of set-valued maps via the Minkowski difference, obtain some relations among the maps and the subdifferential, and establish optimality conditions, weak and strong conjugate duality theorems of set-order solutions to set optimization problem. Finally, we apply the main results of the paper to uncertain optimization problems. communicated by Tuyen Van Nguyen.