向量优化问题广义弱有效解的存在性

THE EXISTENCE OF THE GENERALIZED WEAKLY EFFICIENT SOLUTION FOR VECTOR OPTIMIZATION PROBLEM

主要研究向量优化问题广义弱有效解的存在性,利用广义弱有效解和广义向量平衡问题解的特殊关系,从广义向量平衡问题的结果入手,通过相应条件的转化,得到了广义弱有效解在可行集有界时的存在结果.进而,通过对目标函数和可行集的渐近分析,将这个结果推广至可行集无界的情形,此时目标函数是拟单调的.

In this paper, we mainly consider the existence of the generalized weakly efficient solution for Vector Optimization Problem. Since generalized weakly efficient solution can be seen as a particular solution for Generalized Vector Equilibrium Problem, we may begin and study with Generalized Vector Equilibrium Problem. Using some transformation, we obtain the existence of the generalized weakly efficient solution in the case that the feasible set is bounded. Hence, using asymptotic analysis on the objective function and the feasible set, we generalized this result to the case that the feasible set is unbounded, where, the objective function is generalized quasimonotone.