一类约束多目标优化问题弱有效解的一个择一定理

An Alternative Theorem for a Class of Cone Constrained Multiobjective Optimization Problems

利用像空间分析理论研究一类锥约束多目标优化问题的最优性条件,通过定向距离函数引入一类正则弱分离函数,建立了一个择一定理.最后,通过择一定理在不涉及函数凸性的条件下得到了锥约束多目标优化问题弱有效解的充分和必要最优性条件.

Multiobjective optimization is a common problem in economic management and game theory.However,a great number of practical economic management problems are subject to the constraints of external and internal conditions.That is why constrained multiobjective optimization problems have aroused wide concern.Optimality conditions of multiobjective optimization problems are one of the important contents in the optimization theory.This paper is devoted to the study of the optimality conditions of a class of cone constrained multiobjective optimization problems by image space analysis.A class of regular weak separation functions is introduced by the oriented distance function,and an alternative theorem is established.Finally,some sufficient and necessary optimality conditions for cone constrained multiobjective optimization problems are obtained by the alternative theorem,without the convexity of the involved mappings.