Consider the variational inequality of finding a point satisfying the property , for all , where is the intersection of finite level sets of convex functions defined on a real Hilbert space and is an -Lipschitzian and -strongly monotone operator. Relaxed and self-adaptive iterative algorithms are devised for computing the unique solution of . Since our algorithm avoids calculating the projection (calculating by computing several sequences of projections onto half-spaces containing the original domain ) directly and has no need to know any information of the constants and , the implementation of our algorithm is very easy. To prove strong convergence of our algorithms, a new lemma is established, which can be used as a fundamental tool for solving some nonlinear problems.
"Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/942315