Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities

Authors:
Paul Tseng
Affiliations:
-
Venue:
SIAM Journal on Optimization
Year:
1997

Citing 0
Cited 21

Local convergence analysis of projection-type algorithms: unified approach

Journal of Optimization Theory and Applications
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 hybrid entropic proximal decomposition method with self-adaptive strategy for solving variational inequality problems

Computers & Mathematics with Applications
The over-relaxed proximal point algorithm based on H-maximal monotonicity design and applications

Computers & Mathematics with Applications
Generalized Eckstein-Bertsekas proximal point algorithm based on A-maximal monotonicity design

Computers & Mathematics with Applications
A new relaxed proximal point procedure and applications to nonlinear variational inclusions

Computers & Mathematics with Applications
An improved prediction-correction method for monotone variational inequalities with separable operators

Computers & Mathematics with Applications
An improved proximal alternating direction method for monotone variational inequalities with separable structure

Computational Optimization and Applications
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science

SIAM Journal on Imaging Sciences
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods

SIAM Journal on Matrix Analysis and Applications
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations

SIAM Journal on Optimization
Inexact Alternating Direction Methods for Image Recovery

SIAM Journal on Scientific Computing
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

Foundations and Trends® in Machine Learning
Alternating Direction Method for Covariance Selection Models

Journal of Scientific Computing
The generalized relaxed proximal point algorithm involving A-maximal-relaxed accretive mappings with applications to Banach spaces

Mathematical and Computer Modelling: An International Journal
Generalized Eckstein-Bertsekas proximal point algorithm involving (H,η)-monotonicity framework

Mathematical and Computer Modelling: An International Journal
Generalized over-relaxed proximal algorithm based on A-maximal monotonicity framework and applications to inclusion problems

Mathematical and Computer Modelling: An International Journal
New decomposition methods for solving variational inequality problems

Mathematical and Computer Modelling: An International Journal
Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems

Computational Optimization and Applications
A proximal parallel splitting method for minimizing sum of convex functions with linear constraints

Journal of Computational and Applied Mathematics
An alternating structured trust region algorithm for separable optimization problems with nonconvex constraints

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a mixed problem composed in part of finding a zero of a maximal monotone operator and in part of solving a monotone variational inequality problem. We propose a solution method for this problem that alternates between a proximal step (for the maximal monotone operator part) and a projection-type step (for the monotone variational inequality part) and analyze its convergence and rate of convergence. This method extends a decomposition method of Chen and Teboulle [Math. Programming, 64 (1994), pp. 81--101] for convex programming and yields, as a by-product, new decomposition methods.