Letter to the editor: Extragradient methods for solving nonconvex variational inequalities

  • Authors:

  • Muhammad Aslam Noor;Eisa Al-Said;Khalida Inayat Noor;Yonghong Yao

  • Affiliations:

  • Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan and Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia;Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia;Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan;Mathematics Department, Tianjin Polytechnic University, Tianjin 300160, China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2011

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Abstract

In this paper, we introduce and consider a new class of variational inequalities, which are called the nonconvex variational inequalities. Using the projection technique, we suggest and analyze an extragradient method for solving the nonconvex variational inequalities. We show that the extragradient method is equivalent to an implicit iterative method, the convergence of which requires only pseudo-monotonicity, a weaker condition than monotonicity. This clearly improves on the previously known result. Our method of proof is very simple as compared with other techniques.