Inexact Proximal Point Methods in Metric Spaces

被引：6

作者：

Zaslavski, Alexander J. ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2011年 / 19卷 / 04期

关键词：

Computational error; Metric space; Nonconvex programming; Proximal method; Well-posed problem; MAXIMAL MONOTONE-OPERATORS; COMPUTATIONAL ERRORS; WELL-POSEDNESS; BANACH-SPACES; VARIATIONAL INEQUALITY; NONCONVEX OPTIMIZATION; VECTOR OPTIMIZATION; ALGORITHM; CONVERGENCE;

D O I：

10.1007/s11228-011-0185-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the local convergence of a proximal point method in a metric space under the presence of computational errors. We show that the proximal point method generates a good approximate solution if the sequence of computational errors is bounded from above by some constant. The principle assumption is a local error bound condition which relates the growth of an objective function to the distance to the set of minimizers introduced by Hager and Zhang (SIAM J Control Optim 46:1683-1704, 2007).

引用

页码：589 / 608

页数：20

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