A Direct Splitting Method for Nonsmooth Variational Inequalities

J. Y. Bello Cruz () and R. Díaz Millán ()
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J. Y. Bello Cruz: IME, Federal University of Goiás, Campus Samambaia, CEP 74001-970
R. Díaz Millán: Federal Institute of Education, Science and Technology

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 3, No 3, 728-737

Abstract: Abstract We propose a direct splitting method for solving a nonsmooth variational inequality 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 strongly explores 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 difficulty of other schemes for solving this kind of problem.

Keywords: Maximal monotone operators; Monotone variational inequalities; Projection methods; Splitting methods (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-013-0478-2

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