Robustness of the hybrid extragradient proximal-point algorithm

The hybrid extragradient proximal-point method recently proposed by Solodov and Svaiter has the distinctive feature of allowing a relative error tolerance. We extend the error tolerance of this method, proving that it converges even if a summable error is added to the relative error. Furthermore, th...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 111; no. 1; pp. 117 - 136
Main Authors BURACHIK, R. S, SCHEIMBERG, S, SVAITER, B. F
Format Journal Article
LanguageEnglish
Published New York, NY Springer 01.10.2001
Springer Nature B.V
Subjects
Algorithms
Applied sciences
Approximation
Calculus of variations and optimal control
Computer science; control theory; systems
Control theory. Systems
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Methods
Optimal control
Optimization
Physics
Weak convergence
Global convergence
Algorithms
Hybrid method
Error tolerence
Hybrid
Relative error
Robustness
Proximal point method
Convergence
Convergence analysis
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Summary:The hybrid extragradient proximal-point method recently proposed by Solodov and Svaiter has the distinctive feature of allowing a relative error tolerance. We extend the error tolerance of this method, proving that it converges even if a summable error is added to the relative error. Furthermore, the extragradient step may be performed inexactly with a summable error. We present a convergence analysis, which encompasses other well-known variations of the proximal-point method, previously unrelated. We establish weak global convergence under mild assumptions.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0022-3239
1573-2878
DOI:10.1023/A:1017523331361