Some Methods Based on the D-Gap Function for Solving Monotone Variational Inequalities

Authors:
Michael V. Solodov;Paul Tseng
Affiliations:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ, 22460-320, Brazil. solodov@impa.br;Department of Mathematics, University of Washington, Seattle, WA 98195, USA. tseng@math.washington.edu
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

The D-gap function has been useful in developing unconstrained descent methods for solving strongly monotone variational inequality problems. We show that the D-gap function has certain properties that are useful also for monotone variational inequality problems with bounded feasible set. Accordingly, we develop two unconstrained methods based on them that are similar in spirit to a feasible method of Zhu and Marcotte based on the regularized-gap function. We further discuss a third method based on applying the D-gap function to a regularized problem. Preliminary numerical experience is also reported.