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Regularized Nonconvex Mixed Variational Inequalities: Auxiliary Principle Technique and Iterative Methods

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In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the… Click to show full abstract

In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the auxiliary principle technique, some new predictor corrector methods for solving such class of regularized nonconvex mixed variational inequalities are suggested and analyzed. The study of convergence analysis of the proposed iterative algorithms requires either pseudomonotonicity or partially mixed relaxed and strong monotonicity of the operator involved in regularized nonconvex mixed variational inequalities. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature.

Keywords: principle technique; regularized nonconvex; auxiliary principle; variational inequalities; mixed variational; nonconvex mixed

Journal Title: Journal of Optimization Theory and Applications
Year Published: 2017

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