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<p>This paper is devoted to the study of optimality conditions at infinity in nonsmooth minimax programming problems and their applications. By means of the limiting subdifferential and the normal cone at infinity, we derive necessary and sufficient optimality conditions of the Karush–Kuhn–Tucker type for nonsmooth minimax programming problems with constraints. The obtained results are applied to nonsmooth vector optimization problems and robust minimax optimization ones.</p>

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Optimality Conditions at Infinity for Nonsmooth Minimax Programming Problems with Some Applications

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Nguyen Van Tuyen,
  • Kwan Deok Bae,
  • Do Sang Kim

摘要

This paper is devoted to the study of optimality conditions at infinity in nonsmooth minimax programming problems and their applications. By means of the limiting subdifferential and the normal cone at infinity, we derive necessary and sufficient optimality conditions of the Karush–Kuhn–Tucker type for nonsmooth minimax programming problems with constraints. The obtained results are applied to nonsmooth vector optimization problems and robust minimax optimization ones.