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Vietnam Journal of Mathematics 38:4 (2010) 413-423

 

A Proximal Point-Type Algorithm for Multivalued Variational Inequalities

P. N. Anh, J. K. Kim, D. T. Binh and D. H. Phuc

 

Abstract. We present a new method for solving multivalued variational inequalities. The method is based on a proximal point algorithm with M which is a positive definite matrix but not necessarily symmetric. We first solve monotone multivalued variational inequalities satifying a nonlipschitzian assumption and prove the convergence of the proposed algorithm. Next, we couple this technique with the Banach contraction method for the multivalued variational inequalities. Finally some preliminary computional results are given.

2000 Mathematics Subject Classification: 65K10, 90C25.

Keywords: Multivalued variational inequalities, proximal point-type algorithm, mononicity, linear proximal function, Banach contraction method.

 

 

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