自由支配集下近似平衡约束向量优化问题的稳定性研究

Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets

在自由支配集下,对一类近似平衡约束向量优化问题(AOPVF)的稳定性进行研究.首先,在较弱的凸性假设下获得了约束集映射的Berge-半连续性和约束集的闭性、凸性和紧性结果.然后,在目标函数列Gamma-收敛的假设下,分别得到了AOPVF弱有效解映射Berge-半连续和弱有效解集下Painlevé-Kuratowski收敛的充分条件,并给出例子说明结论是新颖和有意义的.

The stability of vector optimization problems under approximate equilibrium constraints(AOPVF)via free-disposal sets was discussed.Firstly,the Berge-semicontinuity of the constraint set mapping and the closedness,the convexity and the compactness of the constraint set were obtained with the weaker convexity assumption.Moreover,under the assumption of Gamma-convergence for the objective functional sequences,the lower Painlevé-Kuratowski convergence of the weak efficient solution set and the Berge-semicontinuity of weak efficient solution mappings for AOPVF were obtained respectively.Some examples illustrate that the results are new and meaningful.