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

Nguyen Tuyen (), Kwan Deok Bae () and Do Sang Kim ()
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Nguyen Tuyen: Hanoi Pedagogical University 2
Kwan Deok Bae: Pukyong National University
Do Sang Kim: Pukyong National University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 13, 22 pages

Abstract: Abstract 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.

Keywords: Minimax programming; Optimality at infinity; Limiting subdifferential at infinity; Normal cone at infinity; Vector optimization; Robust minimax optimization; 90C47; 49K35; 49J52; 90C29; 90C31 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02652-1

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