On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints

被引：101

作者：

Censor, Yair ^{[1
]}

Chen, Wei ^{[2
]}

Combettes, Patrick L. ^{[3
]}

Davidi, Ran ^{[2
]}

Herman, Gabor T. ^{[2
]}

机构：

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[2] CUNY, Grad Ctr, Dept Comp Sci, New York, NY 10016 USA

[3] Univ Paris 06, UPMC, UMR 7598, Lab Jacques Louis Lions,CNRS, F-75005 Paris, France

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2012年 / 51卷 / 03期

关键词：

Projection methods; Convex feasibility problems; Numerical evaluation; Optimization; Linear inequalities; Sparse matrices; IMAGE-RECONSTRUCTION; STRONG-CONVERGENCE; SPARSE SYSTEMS; FIXED-POINTS; SET; ALGORITHMS; RESTORATION; RECOVERY; BEHAVIOR;

D O I：

10.1007/s10589-011-9401-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they often have a computational advantage over alternatives that have been proposed for solving the same problem and that this makes them successful in many real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of unknowns satisfying up to hundreds of thousands of constraints) and by a discussion of the demonstrated efficacy of projection methods in numerous scientific publications and commercial patents (dealing with problems that can have over a billion unknowns and a similar number of constraints).

引用

页码：1065 / 1088

页数：24

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