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Finite Convergence of the Proximal Point Algorithm for Variational Inequality Problems

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Abstract

In this paper, we establish sufficient conditions for guaranteeing finite termination of an arbitrary algorithm for solving a variational inequality problem in a Banach space. Applying these conditions, it shows that sequences generated by the proximal point algorithm terminate at solutions in a finite number of iterations.

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Authors and Affiliations

  1. Department of Electronics and Information Systems, Akita Prefectural University, 84-4 Yuri-Honjo, Akita, Japan

    Shin-ya Matsushita & Li Xu

Authors
  1. Shin-ya Matsushita
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  2. Li Xu
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Corresponding author

Correspondence to Shin-ya Matsushita.

Additional information

The first author was partially supported by Grant-in-Aid for Young Scientists (B) No. 20740084, the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Matsushita, Sy., Xu, L. Finite Convergence of the Proximal Point Algorithm for Variational Inequality Problems. Set-Valued Var. Anal 21, 297–309 (2013). https://doi.org/10.1007/s11228-012-0225-0

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  • DOI: https://doi.org/10.1007/s11228-012-0225-0

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