Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 159, Issue 1, Pages 192-209Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-012-0252-x
Keywords
Regularized non-convex variational inequalities; Iterative method; Non-convex sets; Prox-regularity; Convergence analysis
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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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