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- Title
A Direct Splitting Method for Nonsmooth Variational Inequalities.
- Authors
Bello Cruz, J.; Díaz Millán, R.
- 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.
- Subjects
SPLITTING extrapolation method; VARIATIONAL inequalities (Mathematics); HILBERT space; STOCHASTIC convergence; MONOTONE operators; ITERATIVE methods (Mathematics)
- Publication
Journal of Optimization Theory & Applications, 2014, Vol 161, Issue 3, p728
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-013-0478-2