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A Projection‐Type Method for Multivalued Variational Inequality

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  • Changjie Fang
  • Shenglan Chen
  • Jiming Zheng

Abstract

We propose a projection‐type method for multivalued variational inequality. The iteration sequence generated by the algorithm is proven to be globally convergent to a solution, provided that the multivalued mapping is continuous with nonempty compact convex values. Moreover, we present a necessary and sufficient condition on the nonemptiness of the solution set. Preliminary computational experience is also reported.

Suggested Citation

  • Changjie Fang & Shenglan Chen & Jiming Zheng, 2013. "A Projection‐Type Method for Multivalued Variational Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:836720
    DOI: 10.1155/2013/836720
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    References listed on IDEAS

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    1. M. Li & L. Z. Liao & X. M. Yuan, 2009. "Proximal Point Algorithms for General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 125-145, July.
    2. Romesh Saigal, 1976. "Extension of the Generalized Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 260-266, August.
    3. E. Allevi & A. Gnudi & I. Konnov, 2006. "The Proximal Point Method for Nonmonotone Variational Inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 553-565, July.
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