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Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities

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Optimization with Multivalued Mappings

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 2))

Summary

We show how to choose regularization parameters such that the solution of a multivalued strongly monotone mixed variational inequality can be obtained by computing the fixed point of a certain multivalued mapping having a contraction selection. Moreover a solution of a multivalued cocoercive variational inequality can be computed by finding a fixed point of a certain mapping having nonexpansive selection. By the Banach contraction mapping principle it is easy to establish the convergence rate.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Pham Ngoc Anh

  2. Optimization and Control Department, Institute of Mathematics, Hanoi, Vietnam

    Dung Le Muu

Authors
  1. Pham Ngoc Anh
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  2. Dung Le Muu
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Editor information

Editors and Affiliations

  1. TU Bergakademie Freiberg, Germany

    Stephan Dempe

  2. ITESM, Monterrey, Mexico

    Vyacheslav Kalashnikov

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© 2006 Springer Science + Business Media, LLC

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Anh, P.N., Le Muu, D. (2006). Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities. In: Dempe, S., Kalashnikov, V. (eds) Optimization with Multivalued Mappings. Springer Optimization and Its Applications, vol 2. Springer, Boston, MA . https://doi.org/10.1007/0-387-34221-4_11

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