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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Vydané v:Journal of optimization theory and applications Ročník 205; číslo 2; s. 32
Hlavní autori: Van Tuyen, Nguyen, Bae, Kwan Deok, Kim, Do Sang
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.05.2025
Springer Nature B.V
Predmet:
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
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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.
AbstractList 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.
ArticleNumber 32
Author Van Tuyen, Nguyen
Bae, Kwan Deok
Kim, Do Sang
Author_xml – sequence: 1
  givenname: Nguyen
  surname: Van Tuyen
  fullname: Van Tuyen, Nguyen
  organization: Department of Mathematics, Hanoi Pedagogical University 2
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  givenname: Kwan Deok
  surname: Bae
  fullname: Bae, Kwan Deok
  organization: Department of Applied Mathematics, Pukyong National University
– sequence: 3
  givenname: Do Sang
  orcidid: 0000-0003-4191-2295
  surname: Kim
  fullname: Kim, Do Sang
  email: dskim@pknu.ac.kr
  organization: Department of Applied Mathematics, Pukyong National University
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Copyright Springer Nature B.V. May 2025
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Keywords 90C31
Limiting subdifferential at infinity
Normal cone at infinity
Minimax programming
90C47
49J52
Robust minimax optimization
90C29
Optimality at infinity
Vector optimization
49K35
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SubjectTerms 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
Title Optimality Conditions at Infinity for Nonsmooth Minimax Programming Problems with Some Applications
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