An Algorithm for Vector Optimization Problems

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Abstract

In this paper, we consider of finding efficient solution and weakly efficient solution for nonconvex vector optimization problems. When X and Y are normed spaces, F is an anti-Lipschitz mapping from X to Y, and the ordering cone is regular, we present an algorithm to guarantee that the generated sequence converges to an efficient solution with respect to normed topology. If the domain of the mapping is compact, we prove that the generated sequence converges to an efficient solution with respect to normed topology without requiring that mapping is anti-Lipschitz. We also give an algorithm to guarantee that the generated sequence converges to a weakly efficient solution with respect to normed topology.

Keywords

Vector optimization problems Efficient solution Weakly efficient solution Algorithm 

Mathematics Subject Classification

90C26 90C29 
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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of MathematicsNanchang UniversityNanchangChina

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