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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 63, 2014 - Issue 4
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A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality

Yonghong Yao Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China
,
Giuseppe Marino Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), ItalyCorrespondence[email protected]
&
Luigi Muglia Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy
Pages 559-569 | Received 24 Oct 2011, Accepted 07 Mar 2012, Published online: 16 May 2012
 
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Abstract

In this article, we propose a modified Korpelevich's method for solving variational inequalities. Under some mild assumptions, we show that the suggested method converges strongly to the minimum-norm solution of some variational inequality in an infinite-dimensional Hilbert space.

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