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

作者:Bello Cruz J Y; Santos P S M; Scheimberg S*
来源:Journal of Optimization Theory and Applications, 2013, 159(3): 562-575.
DOI:10.1007/s10957-012-0181-8

摘要

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.

  • 出版日期2013-12

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