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A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities

  • T. Q. Bao
  • P. Q. Khanh
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 77)

Abstract

We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, closed, lower hemicontinuous, and bounded on each bounded subset (it is not necessarily continuous). Some numerical test problems are implemented by using MATLAB with encouraging effectiveness.

Keywords

Variational inequalities multifunctions projections pseudo monotonicity closedness lower hemicontinuity boundedness 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • T. Q. Bao
    • 1
  • P. Q. Khanh
    • 2
  1. 1.Department of MathematicsWayne State UniversityUSA
  2. 2.Department of Mathematics, International UniversityVietnam National University of Hochiminh CityVietnam

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