A Two-Phase Algorithm for a Variational Inequality Formulation of Equilibrium Problems |
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Authors: | J. Y. Bello Cruz P. S. M. Santos S. Scheimberg |
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Affiliation: | 1. Universidade Federal de Goiás, Goiania, Brazil 2. Universidade Federal Piauí, Teresina, Brazil 3. PESC/COPPE—Programa de Engenharia de Sistemas e Computa??o, IM-Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
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Abstract: | We introduce an explicit algorithm for solving nonsmooth equilibrium problems in finite-dimensional spaces. A particular iteration proceeds in two phases. In the first phase, an orthogonal projection onto the feasible set is replaced by projections onto suitable hyperplanes. In the second phase, a projected subgradient type iteration is replaced by a specific projection onto a halfspace. We prove, under suitable assumptions, convergence of the whole generated sequence to a solution of the problem. The proposed algorithm has a low computational cost per iteration and, some numerical results are reported. |
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