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Construction algorithms for a class of monotone variational inequalities

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Abstract

This paper is devoted to solve the following monotone variational inequality of finding \(x^*\in \mathrm{Fix}(T)\) such that

$$\begin{aligned} \langle Ax^*,x-x^*\rangle \ge 0,\quad \forall x\in \mathrm{Fix}(T), \end{aligned}$$

where A is a monotone operator and \(\mathrm{Fix}(T)\) is the set of fixed points of nonexpansive operator T. For this purpose, we construct an implicit algorithm and prove its convergence hierarchical to the solution of above monotone variational inequality.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China

    Yonghong Yao

  2. Faculty of Applied Sciences, University “Politehnica” of Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania

    Mihai Postolache

  3. Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan

    Yeong-Cheng Liou

  4. Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Yeong-Cheng Liou

  5. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing, 211171, China

    Zhangsong Yao

Authors
  1. Yonghong Yao
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  2. Mihai Postolache
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  3. Yeong-Cheng Liou
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  4. Zhangsong Yao
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Correspondence to Mihai Postolache.

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Yao, Y., Postolache, M., Liou, YC. et al. Construction algorithms for a class of monotone variational inequalities. Optim Lett 10, 1519–1528 (2016). https://doi.org/10.1007/s11590-015-0954-8

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  • DOI: https://doi.org/10.1007/s11590-015-0954-8

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