Adaptive Two-Stage Bregman Method for Variational Inequalities

The authors analyze the two-stage Popov method with Bregman divergence and a new adaptive rule for choosing the step size, which does not require the Lipschitz constants to be known and operator values at additional points to be calculated. For variational inequalities with pseudo-monotone and Lipsc...

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Bibliographic Details
Published inCybernetics and systems analysis Vol. 57; no. 6; pp. 959 - 967
Main Authors Semenov, V. V., Denisov, S. V., Kravets, A. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2021
Springer
Springer Nature B.V
Subjects
Algorithms
Analysis
Artificial Intelligence
Control
Divergence
Equality
Inequalities
Machine learning
Management science
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
variational inequality
pseudo-monotonicity
adaptivity
two-stage method
convergence
Bregman divergence
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Summary:The authors analyze the two-stage Popov method with Bregman divergence and a new adaptive rule for choosing the step size, which does not require the Lipschitz constants to be known and operator values at additional points to be calculated. For variational inequalities with pseudo-monotone and Lipschitz continuous operators acting in a finite-dimensional normed linear space, the convergence theorem for the method is proved.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-021-00421-2