A Relaxed Projection Method for Split Variational Inequalities

Hongjin He (), Chen Ling () and Hong-Kun Xu ()
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Hongjin He: Hangzhou Dianzi University
Chen Ling: Hangzhou Dianzi University
Hong-Kun Xu: National Sun Yat-sen University

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 10, 213-233

Abstract: Abstract We study the recently introduced split variational inequality under the framework of variational inequalities in a product space. The feature of our equivalent formulation of split variational inequality is its variable separability (that is, splitting nature) together with a linear constraint. We propose a relaxed projection method, which fully exploits the splitting structure of split variational inequality and which is not only easily implementable, but also globally convergent under some mild conditions. Our numerical results on finding the minimum-norm solution of the split feasibility problem and on solving a separable and convex quadratic programming problem verify the efficiency and stability of our new method.

Keywords: Split variational inequality; Projection method; Monotone operator; Split feasibility problem; Separable structure; 65K15; 49J40; 90C25; 47J25 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-014-0598-3

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