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Volume
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Vietnam
Journal of Mathematics 38:4 (2010) 413-423
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A Proximal Point-Type Algorithm for Multivalued
Variational Inequalities
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P. N. Anh, J. K.
Kim, D. T. Binh and D. H. Phuc
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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.
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2000 Mathematics Subject Classification: 65K10, 90C25.
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Keywords: Multivalued variational inequalities,
proximal point-type algorithm, mononicity, linear proximal function, Banach
contraction method.
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