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  • Research Article
  • Open Access

Algorithms Construction for Variational Inequalities

Fixed Point Theory and Applications20112011:794203

https://doi.org/10.1155/2011/794203

  • Received: 4 October 2010
  • Accepted: 19 February 2011
  • Published:

Abstract

We devote this paper to solving the variational inequality of finding with property such that for all . Note that this hierarchical problem is associated with some convex programming problems. For solving the above VI, we suggest two algorithms: Implicit Algorithmml: for all and Explicit Algorithm: for all . It is shown that these two algorithms converge strongly to the unique solution of the above VI. As special cases, we prove that the proposed algorithms strongly converge to the minimum norm fixed point of .

Keywords

  • Variational Inequality
  • Differential Geometry
  • Computational Biology
  • Full Article
  • Algorithm Construction

Publisher note

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Authors’ Affiliations

(1)
Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China
(2)
Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan
(3)
Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Republic of Korea

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