Convergent Algorithm Based on Progressive Regularization for Solving Pseudomonotone Variational Inequalities

N. El Farouq
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N. El Farouq: Université Blaise Pascal

Journal of Optimization Theory and Applications, 2004, vol. 120, issue 3, No 1, 455-485

Abstract: Abstract In this paper, we extend the Moreau-Yosida regularization of monotone variational inequalities to the case of weakly monotone and pseudomonotone operators. With these properties, the regularized operator satisfies the pseudo-Dunn property with respect to any solution of the variational inequality problem. As a consequence, the regularized version of the auxiliary problem algorithm converges. In this case, when the operator involved in the variational inequality problem is Lipschitz continuous (a property stronger than weak monotonicity) and pseudomonotone, we prove the convergence of the progressive regularization introduced in Refs. 1, 2.

Keywords: Variational inequalities; generalized monotonicity; pseudomonotonicity; regularization; convergence of algorithms; decomposition. (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTA.0000025706.49562.08

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