Aubin property for solution set in multi-objective programming

Morteza Rahimi () and Majid Soleimani-damaneh ()
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Morteza Rahimi: University of Tehran
Majid Soleimani-damaneh: University of Tehran

Journal of Global Optimization, 2023, vol. 85, issue 2, No 7, 460 pages

Abstract: Abstract 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.

Keywords: Variational analysis; Perturbation in optimization; Multi-objective programming; Aubin stability; Tilt-stability; Full-stability; 90C29; 49J52; 90C31 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01209-0

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