Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems
Zhibin Liu, JongKyu Kim, Nan‐jing Huang · Journal of Inequalities and Applications · 2008
We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmooth vector optimization problems by using the equivalence and Fan-KKM theorem under some suitable conditions.