Abstract
A variational inequality with a nonmonotone mapping is considered in a Euclidean space. A regularization method with respect to some of the variables is proposed for its solution. The convergence of the method is proved under a coercivity-type condition. The method is applied to an implicit optimization problem with an arbitrary perturbing mapping. The solution technique combines partial regularization and the dual descent method.
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Original Russian Text © D.A. Dyabilkin, I.V. Konnov, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 3, pp. 355–364.
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Dyabilkin, D.A., Konnov, I.V. Partial regularization method for nonmonotone variational inequalities. Comput. Math. and Math. Phys. 48, 337–345 (2008). https://doi.org/10.1134/S0965542508030019
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DOI: https://doi.org/10.1134/S0965542508030019