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A direct splitting method for nonsmooth variational inequalities

J.Y. Bello Cruz(yunier***at***impa.br)
R. Díaz Millán(rdiazmillan***at***gmail.com)

Abstract: We propose a direct splitting method for solving nonsmooth variational inequality problems in Hilbert spaces. The weak convergence is established, when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which explores strongly the structure of the operator using projected subgradient-like techniques. The advantage of our method is that any nontrivial subproblem must be solved, like the evaluation of the resolvent operator. The necessity to compute proximal iterations is the main difficult of others schemes for solving this kind of problem.

Keywords: Maximal monotone operators · Monotone variational inequalities · Projection methods · Splitting methods

Category 1: Complementarity and Variational Inequalities

Category 2: Convex and Nonsmooth Optimization

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 07/26/2013
Entry Accepted: 07/26/2013
Entry Last Modified: 07/26/2013

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