An Explicit Parallel Algorithm for Variational Inequalities
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The paper proposes an explicit parallel iterative algorithm for solving variational inequalities over the intersection of fixed point sets of finitely many demicontractive mappings. The algorithm combines the steepest descent method with the Krasnosel’skii–Mann type method and the splitting-up technique. The strongly convergent theorem is established under fewer restrictions imposed on parameters and mappings. Several applications of the algorithm to other problems are presented. We also illustrate the convergence of the algorithm and compare it with others by considering some preliminary numerical experiments.
KeywordsVariational inequality Demicontractive mapping Nonexpansive mapping Parallel computation
Mathematics Subject Classification65J15 47H05 47J25 47J20
The author would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in presenting and improving the original version of this paper. The guidance of Profs. P. K. Anh and L. D. Muu is gratefully acknowledged.
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