Proximal Point Approach and Approximation of Variational Inequalities

Authors:
A. Kaplan;R. Tichatschke
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2000

Citing 0
Cited 4

Auxiliary Problem Principle and Proximal Point Methods

Journal of Global Optimization
Convergence analysis of non-quadratic proximal methods for variational inequalities in Hilbert spaces

Journal of Global Optimization
Some recent advances in projection-type methods for variational inequalities

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
A Parallel Splitting Method for Coupled Monotone Inclusions

SIAM Journal on Control and Optimization

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Abstract

A general approach to analyze convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation of the variational inequality with the proximal point algorithm as well as to related methods using regularization on a subspace and weak regularization. This approach also covers so-called multistep regularization methods, in which the number of proximal iterations in the approximated problems is controlled by a criterion characterizing these iterations as to be effective. The conditions on convergence require control of the exactness of the approximation only in a certain region of the original space. Conditions ensuring linear convergence of the methods are established.