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

✍ Scribed by Zhe Chen; Haiqiao Huang; Kequan Zhao

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 485 KB
Volume: 57
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2008.11.017

No coin nor oath required. For personal study only.

✦ Synopsis

Pareto optimal solution

Error term a b s t r a c t

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.

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