向量优化问题Benson真有效解的稳定性

Abstract

Abstract:

In this paper, at the beginning, we established the equivalent relationship between Benson proper efficient solutions of vector optimization problems and the solution of a class of scalar optimization problems by using nonlinear scaling technique. Besides, with the means of the equivalence result, we obtained the anti-interference stability results of Benson proper efficient point sets and the solution sets in the vector optimization problem when the objective function and the constraint conditions were perturbed. For the first time, by the means of the scalarization technique, we study the anti-interference of Benson proper efficient solutions of vector optimization problems under the condition that the disturbance problem sequence Painlevé-Kuratowski converges to the object optimization problem. And the results have important theoretical value for numerical calculation and analysis.

Key words: Benson proper efficient solution, Painlevé-Kuratowski convergence, Scalarization, Stability

CLC Number:

O224

Jing Zeng,Ruiting Hu. Stability of Benson Proper Efficient Solutions for Vector Optimization Problems[J].Acta mathematica scientia,Series A, 2022, 42(1): 35-44.

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References 21

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Stability of Benson Proper Efficient Solutions for Vector Optimization Problems

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