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

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 205; no. 2; p. 32
Main Authors: Van Tuyen, Nguyen, Bae, Kwan Deok, Kim, Do Sang
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2025
Springer Nature B.V
Subjects:
Applications of Mathematics
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Euclidean space
Infinity
Mathematical functions
Mathematics
Mathematics and Statistics
Minimax technique
Operations Research/Decision Theory
Optimization
Programming
Theory of Computation
90C31
Limiting subdifferential at infinity
Normal cone at infinity
Minimax programming
90C47
49J52
Robust minimax optimization
90C29
Optimality at infinity
Vector optimization
49K35
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02652-1