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Approximate proximal methods in vector optimization
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DOI：10.1016/j.ejor.2006.09.070.png)
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This paper studies the vector optimization problem of finding weakly efficient points for mappings in a Banach space Y, with respect to the partial order induced by a closed, convex, and pointed cone C subset of Y with a nonempty interior. The proximal method in vector optimization is extended to develop an approximate proximal method for this problem by virtue of the approximate proximal point method for finding a root of a maximal monotone operator. In this approximate proximal method, the subproblems consist of finding weakly efficient points for suitable regularizations of the original mapping. We present both an absolute and a relative version, in which the subproblems are solved only approximately. Weak convergence of the generated sequence to a weak efficient point is established. In addition, we also discuss an extension to Bregman-function-based proximal algorithms for finding weakly efficient points for mappings. (c) 2006 Elsevier B.V. All rights reserved.
Keyword:
vector optimization
proximal point
inexact algorithm
Banach space
期刊
IF:
6
论文数:
2.2W
被引数:
6.4W
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