Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming

In this paper, we perform optimality conditions and sensitivity analysis for parametric nonconvex minimax programming problems. Our aim is to study the necessary optimality conditions by using the Mordukhovich (limiting) subdifferential and to give upper estimations for the Mordukhovich subdifferent...

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Published in:Journal of global optimization Vol. 90; no. 1; pp. 53 - 72
Main Authors: An, D. T. V., Hung, N. H., Ngoan, D. T., Tuyen, N. V.
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2024
Springer
Springer Nature B.V
Subjects:
Approximation
Computer Science
Convex analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Parameter sensitivity
Real Functions
Sensitivity analysis
Theorems
90C31
Optimality conditions
Optimal value function
90C46
90C29
Metric qualification condition
Subdifferentiation of maximum functions
Parametric nonconvex minimax programming
Mordukhovich subdifferentials
49K35
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Abstract In this paper, we perform optimality conditions and sensitivity analysis for parametric nonconvex minimax programming problems. Our aim is to study the necessary optimality conditions by using the Mordukhovich (limiting) subdifferential and to give upper estimations for the Mordukhovich subdifferential of the optimal value function in the problem under consideration. The optimality conditions and sensitivity analysis are obtained by using upper estimates for Mordukhovich subdifferentials of the maximum function. The results on optimality conditions are then applied to parametric multiobjective optimization problems. An example is given to illustrate our results.
AbstractList In this paper, we perform optimality conditions and sensitivity analysis for parametric nonconvex minimax programming problems. Our aim is to study the necessary optimality conditions by using the Mordukhovich (limiting) subdifferential and to give upper estimations for the Mordukhovich subdifferential of the optimal value function in the problem under consideration. The optimality conditions and sensitivity analysis are obtained by using upper estimates for Mordukhovich subdifferentials of the maximum function. The results on optimality conditions are then applied to parametric multiobjective optimization problems. An example is given to illustrate our results.
Audience Academic
Author An, D. T. V.
Ngoan, D. T.
Hung, N. H.
Tuyen, N. V.
Author_xml – sequence: 1
  givenname: D. T. V.
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  surname: An
  fullname: An, D. T. V.
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  surname: Hung
  fullname: Hung, N. H.
  organization: Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa
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  givenname: D. T.
  surname: Ngoan
  fullname: Ngoan, D. T.
  organization: Department of Basic Sciences, Hanoi University of Natural Resources and Environment
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  givenname: N. V.
  orcidid: 0000-0003-1920-310X
  surname: Tuyen
  fullname: Tuyen, N. V.
  email: tuyensp2@yahoo.com, nguyenvantuyen83@hpu2.edu.vn
  organization: Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa
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Keywords 90C31
Optimality conditions
Optimal value function
90C46
90C29
Metric qualification condition
Subdifferentiation of maximum functions
Parametric nonconvex minimax programming
Mordukhovich subdifferentials
49K35
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SubjectTerms Approximation
Computer Science
Convex analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Parameter sensitivity
Real Functions
Sensitivity analysis
Theorems
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Title Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming
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