On Finite Convergence of Iterative Methods for Variational Inequalities in Hilbert Spaces

Shin-ya Matsushita () and Li Xu
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Shin-ya Matsushita: Akita Prefectural University
Li Xu: Akita Prefectural University

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 3, No 1, 715 pages

Abstract: Abstract In a Hilbert space, we study the finite termination of iterative methods for solving a monotone variational inequality under a weak sharpness assumption. Most results to date require that the sequence generated by the method converges strongly to a solution. In this paper, we show that the proximal point algorithm for solving the variational inequality terminates at a solution in a finite number of iterations if the solution set is weakly sharp. Consequently, we derive finite convergence results for the gradient projection and extragradient methods. Our results show that the assumption of strong convergence of sequences can be removed in the Hilbert space case.

Keywords: Variational inequality; Weak sharp; Proximal point algorithm; Metric projection; Gradient projection method; Extragradient method; Hilbert space (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-013-0460-z

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