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J.Y. Bello Cruz(yunier.bellogmail.com) Abstract: We introduce a relaxedprojection 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 subgradientlike 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: Pointtoset 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 Citation: Download: [PDF] Entry Submitted: 12/13/2013 Modify/Update this entry  
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