A Relaxed-Projection Splitting Algorithm for Variational Inequalities in Hilbert Spaces

J.Y. Bello Cruz(yunier.bellogmail.com)
R. Díaz Millán(rdiazmillangmail.com)

Abstract: We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous convex function inequality. In our scheme, the orthogonal projections onto the feasible set are replaced by projections onto separating hyperplanes. Furthermore, each iteration of the proposed method consists of simple subgradient-like steps, which does not demand the solution of a nontrivial subproblem, using only individual operators, which explores the structure of the problem. Assuming monotonicity of the individual operators and the existence of solutions, we prove that the generated sequence converges weakly to a solution.

Keywords: Point-to-set operator, Projection method, Relaxed method, Splitting methods, Variational inequality problem, Weak convergence.

Category 1: Complementarity and Variational Inequalities

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Nonlinear Optimization

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Entry Submitted: 12/13/2013
Entry Accepted: 12/15/2013
Entry Last Modified: 12/13/2013

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