# A Modified Alternating Direction Method for Variational Inequality Problems

A Modified Alternating Direction Method for Variational Inequality Problems The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results to illustrate the efficiency of the method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A Modified Alternating Direction Method for Variational Inequality Problems

, Volume 45 (1) – Jan 1, 2002
12 pages

/lp/springer_journal/a-modified-alternating-direction-method-for-variational-inequality-iTkhmj0tR0
Publisher
Springer Journals
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-001-0029-3
Publisher site
See Article on Publisher Site

### Abstract

The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results to illustrate the efficiency of the method.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2002

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