不确定多目标优化的鲁棒解及强弱Kuhn-Tucker条件

Robust Solutions and the Weak and Strong Kuhn-Tucker Conditions in Uncertain Multi-Objective Optimization

【目的】对不确定多目标优化问题的鲁棒解及相关性质进行讨论。【方法】基于Burachik定义的两个正则条件,提出两个新的正则条件,即鲁棒性正则条件,进而利用新正则条件对不确定多目标优化问题的鲁棒解进行研究。【结果】建立了该问题鲁棒有效解的弱Kuhn-Tucker必要条件和真鲁棒有效解的强Kuhn-Tucker必要条件。【结论】所得的主要结果是对最近一些研究工作的改进和推广。

[Purposes]To discuss the robust solutions and related properties of uncertain multi-objective optimization problems.[Methods]Based on the two regular conditions defined by Burachik,two new regularity conditions are proposed,namely robust regularity conditions.Furthermore,under the condition of the new regularity,the robust solutions of uncertain multi-objective optimization problems with inequality constraints are studied.[Findings]The weak Kuhn-Tucker necessary condition of robust efficient solutions and strong Kuhn-Tucker necessary condition of Geoffrion properly robust efficient solutions are established.[Conclusions]The main results improve and generalize some recent research works.