A USE OF CONJUGATE GRADIENT DIRECTION FOR THE CONVEX OPTIMIZATION PROBLEM OVER THE FIXED POINT SET OF A NONEXPANSIVE MAPPING

被引：108

作者：

Iiduka, Hideaki ^{[1
]}

Yamada, Isao ^{[2
]}

机构：

[1] Kyushu Inst Technol, Network Design Res Ctr, Chiyoda Ku, Tokyo 1000011, Japan

[2] Tokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528552, Japan

来源：

SIAM JOURNAL ON OPTIMIZATION | 2009年 / 19卷 / 04期

基金：

日本学术振兴会;

关键词：

convex optimization problem; nonexpansive mapping; fixed point; hybrid steepest descent method; conjugate gradient direction; GLOBAL CONVERGENCE; MINIMIZATION;

D O I：

10.1137/070702497

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the convex optimization problem over the fixed point set of a nonexpansive mapping. The main objective of the paper is to accelerate the hybrid steepest descent method for the problem. To this goal, we present a new iterative scheme that utilizes the conjugate gradient direction. Its convergence to the solution is guaranteed under certain assumptions. In order to demonstrate the effectiveness, performance, and convergence of our proposed algorithm, we present numerical comparisons of the algorithm with the existing algorithm.

引用

页码：1881 / 1893

页数：13

共 46 条

[1] DESCENT PROPERTY AND GLOBAL CONVERGENCE OF THE FLETCHER REEVES METHOD WITH INEXACT LINE SEARCH [J].