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<p>This paper introduces a novel derivative concept, the <i>m</i>th-order Studniarski-like derivative, tailored for nonsmooth optimization. We investigate its fundamental properties and develop essential calculus rules. Utilizing this framework, we formulate a mixed-type dual problem for nonsmooth multiobjective semi-infinite optimization problems with mixed constraints. Comprehensive duality results, including weak, strong, and converse duality theorems, are established under suitable assumptions. These results lead to new higher-order strong Karush–Kuhn–Tucker (KKT) optimality conditions for weakly efficient solutions. The proposed approach not only generalizes but also improves several existing results in the literature.</p>

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A mixed type duality for nonsmooth multiobjective semi-infinite problems with mixed constraints

  • 期刊论文

  • 发表日期：

    2025年9月10日

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  • Nguyen Le Hoang Anh,
  • Nguyen Manh Truong Giang,
  • Nguyen Thanh Thoa

摘要

This paper introduces a novel derivative concept, the mth-order Studniarski-like derivative, tailored for nonsmooth optimization. We investigate its fundamental properties and develop essential calculus rules. Utilizing this framework, we formulate a mixed-type dual problem for nonsmooth multiobjective semi-infinite optimization problems with mixed constraints. Comprehensive duality results, including weak, strong, and converse duality theorems, are established under suitable assumptions. These results lead to new higher-order strong Karush–Kuhn–Tucker (KKT) optimality conditions for weakly efficient solutions. The proposed approach not only generalizes but also improves several existing results in the literature.