Abstract
In this paper, we investigate or analyze non-convex variational inequalities and general non-convex variational inequalities. Two new classes of non-convex variational inequalities, named regularized non-convex variational inequalities and general regularized non-convex variational inequalities, are introduced, and the equivalence between these two classes of non-convex variational inequalities and the fixed point problems are established. A projection iterative method to approximate the solutions of general regularized non-convex variational inequalities is suggested. Meanwhile, the existence and uniqueness of solution for general regularized non-convex variational inequalities is proved, and the convergence analysis of the proposed iterative algorithm under certain conditions is studied.
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The author thanks Professor Javad Mashreghi and the anonymous referees for their constructive comments, which contributed to the improvement of the present paper.
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Balooee, J. Projection Method Approach for General Regularized Non-convex Variational Inequalities. J Optim Theory Appl 159, 192–209 (2013). https://doi.org/10.1007/s10957-012-0252-x
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DOI: https://doi.org/10.1007/s10957-012-0252-x