Approximate generalized proximal-type method for convex vector optimization problem in Banach spaces

Authors:
Zhe Chen;Haiqiao Huang;Kequan Zhao
Affiliations:
Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China and Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom Kowloon, ...;School of Fashion Art and Engineering, Beijing Institute of Clothing Technology, Beijing 100029, China;Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, we consider a convex vector optimization problem of finding weak Pareto optimal solutions for an extended vector-valued map from a uniformly convex and uniformly smooth Banach space to a real Banach space, with respect to the partial order induced by a closed, convex and pointed cone with a nonempty interior. We propose an inexact vector-valued proximal-type point algorithm based on a Lyapunov functional when the iterates are computed approximately and prove the sequence generated by the algorithm weakly converges to a weak Pareto optimal solution of the vector optimization problem under some mild conditions. Our results improve and generalize some known results.