A Two-Phase Algorithm for a Variational Inequality Formulation of Equilibrium Problems

J. Y. Bello Cruz (), P. S. M. Santos () and S. Scheimberg ()
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J. Y. Bello Cruz: Universidade Federal de Goiás
P. S. M. Santos: Universidade Federal Piauí
S. Scheimberg: Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 3, No 2, 562-575

Abstract: 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.

Keywords: Equilibrium problem; Projection method; Relaxed method (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0181-8

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