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2013 Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets
Songnian He, Caiping Yang
Abstr. Appl. Anal. 2013: 1-8 (2013). DOI: 10.1155/2013/942315

Abstract

Consider the variational inequality V I ( C , F ) of finding a point x * C satisfying the property F x * , x - x * 0 , for all x C , where C is the intersection of finite level sets of convex functions defined on a real Hilbert space H and F : H H is an L -Lipschitzian and η -strongly monotone operator. Relaxed and self-adaptive iterative algorithms are devised for computing the unique solution of V I ( C , F ) . Since our algorithm avoids calculating the projection P C (calculating P C by computing several sequences of projections onto half-spaces containing the original domain C ) directly and has no need to know any information of the constants L and η , 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.

Citation

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Songnian He. Caiping Yang. "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

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1273.47099
MathSciNet: MR3055865
Digital Object Identifier: 10.1155/2013/942315

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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