Necessary optimality conditions for minimax programming problems with mathematical constraints

In this paper, necessary optimality conditions in terms of upper and/or lower subdifferentials of both cost and constraint functions are derived for minimax optimization problems with inequality, equality and geometric constraints in the setting of non-differentiatiable and non-Lipschitz functions i...

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Published in:Optimization Vol. 66; no. 11; pp. 1755 - 1776
Main Authors: Bao, Truong Q., Gupta, Pankaj, Khanh, Phan Q.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.11.2017
Taylor & Francis LLC
Subjects:
Economic models
Functions (mathematics)
fuzzy necessary optimality conditions
Geometric constraints
lower subdifferential necessary optimality conditions
Mathematical programming
minimax fractional programming
Minimax programming
Minimax technique
Nonlinear programming
upper subdifferential necessary optimality conditions
ISSN:0233-1934, 1029-4945
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Abstract In this paper, necessary optimality conditions in terms of upper and/or lower subdifferentials of both cost and constraint functions are derived for minimax optimization problems with inequality, equality and geometric constraints in the setting of non-differentiatiable and non-Lipschitz functions in Asplund spaces. Necessary optimality conditions in the fuzzy form are also presented. An application of the fuzzy necessary optimality condition is shown by considering minimax fractional programming problem.
AbstractList In this paper, necessary optimality conditions in terms of upper and/or lower subdifferentials of both cost and constraint functions are derived for minimax optimization problems with inequality, equality and geometric constraints in the setting of non-differentiatiable and non-Lipschitz functions in Asplund spaces. Necessary optimality conditions in the fuzzy form are also presented. An application of the fuzzy necessary optimality condition is shown by considering minimax fractional programming problem.
Author Bao, Truong Q.
Khanh, Phan Q.
Gupta, Pankaj
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  givenname: Pankaj
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  organization: Department of Operational Research, University of Delhi
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  givenname: Phan Q.
  surname: Khanh
  fullname: Khanh, Phan Q.
  organization: Department of Mathematics, International University, Vietnam National University
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SubjectTerms Economic models
Functions (mathematics)
fuzzy necessary optimality conditions
Geometric constraints
lower subdifferential necessary optimality conditions
Mathematical programming
minimax fractional programming
Minimax programming
Minimax technique
Nonlinear programming
upper subdifferential necessary optimality conditions
Title Necessary optimality conditions for minimax programming problems with mathematical constraints
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