Aubin property for solution set in multi-objective programming

In this paper, the behavior of the solutions of a multi-objective optimization problem, whose the objective functions are perturbed by adding a small linear term, is analyzed. In this regard, a new notion of Lipschitzian stability, by means of the Aubin property of the solution set, is defined. Lips...

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Bibliographic Details
Published in:Journal of global optimization 2023-02, Vol.85 (2), p.441-460
Main Authors: Rahimi, Morteza, Soleimani-damaneh, Majid
Format: Article
Language:English
Subjects:
Computer Science
Efficiency
Mathematical programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Real Functions
Stability analysis
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Summary:In this paper, the behavior of the solutions of a multi-objective optimization problem, whose the objective functions are perturbed by adding a small linear term, is analyzed. In this regard, a new notion of Lipschitzian stability, by means of the Aubin property of the solution set, is defined. Lipschitz stable locally efficient solutions, as generalization of tilt/full stable solutions, are introduced and characterized by modern variational analysis tools. Applying the weighted sum method, the relationships between these solutions and full-stable local optimal solutions of the scalarized problem are investigated. The key tools in deriving our results come from the first- and second-order variational analysis.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01209-0