Asplund空间中非凸向量均衡问题近似解的最优性条件

Optimality Conditions for Approximate Solutions on Nonconvex Vector Equilibrium Problems in Asplund Spaces

在Asplund空间中,研究了非凸向量均衡问题近似解的最优性条件.借助Mordukhovich次可微概念,在没有任何凸性条件下获得了向量均衡问题εe-拟弱有效解,εe-拟Henig有效解,εe-拟全局有效解以及εe-拟有效解的必要最优性条件.作为它的应用,还给出了非凸向量优化问题近似解的最优性条件.

The purpose of this paper is to study approximate solutions for the vector equilibrium problem in Asplund spaces without any convexity assumption.We obtain optimality conditions for εe-quasi weakly efficient solutions,εe-quasi Henig efficient solutions,εe-quasi globally efficient solutions and εe-quasi efficient solutions to vector equilibrium problems by the Mordukhovich subdifferential.As applications of our results,we derive some optimality conditions for nonconvex vector optimization problems.