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Solving variational inequalities defined on a domain with infinitely many linear constraints

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Abstract

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research Program, North Carolina State University, Raleigh, NC, 26695-7906, USA

    Shu-Cherng Fang

  2. Departments of Mathematical Sciences and Industrial Engineering Program, Tsinghua University, Beijing, 100084, China

    Shu-Cherng Fang

  3. Institute of Applied Mathematics, National Cheng Kung University, Tainan, 700, Taiwan, ROC

    Soonyi Wu

  4. Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, 34956, Turkey

    Ş. İlker Birbil

  5. National Center for Theoretical Sciences, Tainan, Taiwan

    Soonyi Wu

Authors
  1. Shu-Cherng Fang
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  2. Soonyi Wu
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  3. Ş. İlker Birbil
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Corresponding author

Correspondence to Shu-Cherng Fang.

Additional information

The work of S. Wu was partially supported by the National Science Council, Taiwan, ROC (Grant No. 19731001). S.-C. Fang’s research has been supported by the US Army Research Office (Grant No. W911NF-04-D-0003) and National Science Foundation (Grant No. DMI-0553310).

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Fang, SC., Wu, S. & Birbil, Ş.İ. Solving variational inequalities defined on a domain with infinitely many linear constraints. Comput Optim Appl 37, 67–81 (2007). https://doi.org/10.1007/s10589-007-9013-4

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  • DOI: https://doi.org/10.1007/s10589-007-9013-4

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