Projection algorithms for solving convex feasibility problems

被引：1307

作者：

Bauschke, HH

Borwein, JM

机构：

[1] Dept. of Mathematics and Statistics, Simon Fraser University, Burnaby

来源：

SIAM REVIEW | 1996年 / 38卷 / 03期

关键词：

angle between two subspaces; averaged mapping; Cimmino's method; computerized tomography; convex feasibility problem; convex function; convex inequalities; convex programming; convex set; Fejer monotone sequence; firmly nonexpansive mapping; Hilbert space; image recovery; iterative method; Kaczmarz's method; linear convergence; linear feasibility problem; linear inequalities; nonexpansive mapping; orthogonal projection; projection algorithm; projection method; Slater point; subdifferential; subgradient; subgradient algorithm; successive projections;

D O I：

10.1137/S0036144593251710

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

引用

页码：367 / 426

页数：60

共 109 条

[1] THE RELAXATION METHOD FOR LINEAR INEQUALITIES [J].