Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems
© Zhi-Bin Liu et al. 2008
Received: 9 January 2008
Accepted: 4 April 2008
Published: 14 April 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.
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