solving the variational inequality problem defined on intersection of finite level sets

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ID: 155837
2013
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Abstract
Consider the variational inequality VI(C,F) of finding a point x*∈C satisfying the property 〈Fx*,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 VI(C,F). Since our algorithm avoids calculating the projection PC (calculating PC 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.
Reference Key
he2013abstractsolving Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Songnian He;Caiping Yang
Journal science and technology of advanced materials
Year 2013
DOI
10.1155/2013/942315
URL
http://dx.doi.org/10.1155/2013/942315
Keywords
mathematics

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