New Iterative Methods for Solving Exponentially General Regularized Nonconvex Variational Inequality

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Abstract

In this paper, we introduce and study a new class of extended exponentially general regularized nonconvex variational inequalities. We showed that the inequalities are equivalent to fixed-point problems through the use of the projection properties. Based on this equivalence, we discuss the existence and uniqueness of solutions to the extended exponentially general regularized nonconvex variational inequalities. We present a new self-adaptive finite p-step iterative projection scheme that uses multiple updates to obtain common solutions of the extended exponentially general regularized nonconvex variational inequality. Furthermore, we analyze the convergence of this algorithm under various suitable conditions.

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