Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 942315, 8 pages.
Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets
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.
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 942315, 8 pages.
First available in Project Euclid: 27 February 2014
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He, Songnian; Yang, Caiping. Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets. Abstr. Appl. Anal. 2013 (2013), Article ID 942315, 8 pages. doi:10.1155/2013/942315. https://projecteuclid.org/euclid.aaa/1393511882