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Aubin property for solution set in multi-objective programming

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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.

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Notes

  1. See [31] for definition of isolated efficiency.

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Acknowledgements

The authors express their sincere thanks to the handling editor and anonymous referee for their helpful comments. Morteza Rahimi was supported by a grant from Basic Sciences Research Fund (No. BSRF-math-399-04).

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Morteza Rahimi & Majid Soleimani-damaneh

  2. Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

    Morteza Rahimi

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  1. Morteza Rahimi
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  2. Majid Soleimani-damaneh
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Correspondence to Majid Soleimani-damaneh.

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Rahimi, M., Soleimani-damaneh, M. Aubin property for solution set in multi-objective programming. J Glob Optim 85, 441–460 (2023). https://doi.org/10.1007/s10898-022-01209-0

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