کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
479032 | 1446188 | 2007 | 19 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Approximate proximal methods in vector optimization Approximate proximal methods in vector optimization](/preview/png/479032.png)
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 ⊂ 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.
Journal: European Journal of Operational Research - Volume 183, Issue 1, 16 November 2007, Pages 1–19