Minimax programming as a tool for studying robust multi-objective optimization problems

This paper aims to investigate optimality conditions for a weakly Pareto solution to a robust multi-objective optimization problem with locally Lipschitzian data. We do this by using a minimax programming approach , namely, by establishing the necessary optimality condition for a (local) optimal sol...

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Bibliographic Details
Published in:Annals of operations research Vol. 319; no. 2; pp. 1589 - 1606
Main Authors: Hong, Zhe, Bae, Kwan Deok, Kim, Do Sang
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2022
Springer
Springer Nature B.V
Subjects:
Applied mathematics
Business and Management
Combinatorics
Game theory
Integer programming
Linear programming
Mathematical optimization
Mathematical programming
Minimax technique
Multiple objective analysis
Operations research
Operations Research/Decision Theory
Optimization
Original Research
Pareto optimization
Pareto principle
Robustness (mathematics)
Theory of Computation
China
90C46
Minimax programming
KKT optimality conditions
90C25
Multi-objective optimization
Duality
Generalized convexity
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:This paper aims to investigate optimality conditions for a weakly Pareto solution to a robust multi-objective optimization problem with locally Lipschitzian data. We do this by using a minimax programming approach , namely, by establishing the necessary optimality condition for a (local) optimal solution to a robust minimax optimization problem under a suitable constraint qualification, we then employ it to arrive in the desired target. In addition, some duality results for both robust minimax optimization problems and robust multi-objective optimization problems are also provided.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-021-04179-w