The method of cyclic projections for closed convex sets in a Hilbert space under the presence of computational errors

被引：0

作者：

Zaslavski, Alexander J. ^{[1
]}

机构：

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

来源：

NUMERICAL ALGORITHMS | 2022年 / 91卷 / 03期

关键词：

Hilbert space; Inexact product; Infinite product; Nonexpansive mapping; Projection; FEASIBILITY;

D O I：

10.1007/s11075-022-01308-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the method of cyclic projections for inconsistent convex feasibility problems in a Hilbert space under the presence of computational errors. We show that our algorithm generates a good approximate solution, if computational errors are bounded from above by a small positive constant. Our main goal is, for a known computational error, to find out what approximate solution can be obtained and how many iterates one needs for this.

引用

页码：1427 / 1439

页数：13

共 20 条

[1] The method of cyclic projections for closed convex sets in a Hilbert space under the presence of computational errors
Alexander J. Zaslavski
Numerical Algorithms, 2022, 91 : 1427 - 1439
[2] On closed sets with convex projections in Hilbert space
Barov, Stoyu
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FUNDAMENTA MATHEMATICAE, 2007, 197 : 17 - 33
[3] ON CLOSED SETS IN HILBERT SPACE WITH CONVEX PROJECTIONS UNDER SOMEWHERE DENSE SETS OF DIRECTIONS
Barov, Stoyu
Dijkstra, Jan J.
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[4] Projections onto closed convex sets in Hilbert spaces
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[5] Projections onto closed convex sets in Hilbert spaces
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[6] THE EXTRAGRADIENT METHOD FOR CONVEX OPTIMIZATION IN THE PRESENCE OF COMPUTATIONAL ERRORS
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[7] A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space
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[8] CONVERGENCE OF A PROXIMAL POINT METHOD IN THE PRESENCE OF COMPUTATIONAL ERRORS IN HILBERT SPACES
Zaslavski, Alexander J.
SIAM JOURNAL ON OPTIMIZATION, 2010, 20 (05) : 2413 - 2421
[9] The Projected Subgradient Method for Nonsmooth Convex Optimization in the Presence of Computational Errors
Zaslavski, Alexander J.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2010, 31 (05) : 616 - 633
[10] The spaces of compact convex sets and bounded closed convex sets in a Banach space
Sakai, Katsuro
HOUSTON JOURNAL OF MATHEMATICS, 2008, 34 (01): : 289 - 300

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