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arXiv · 1304.0690

An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space

Andrzej Cegielski·Aviv Gibali·Simeon Reich·Rafał Zalas
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Abstract

This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization problem.

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Andrzej Cegielski, Aviv Gibali, Simeon Reich, Rafał Zalas. 2013-04-02. An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space. https://arxiv.org/abs/1304.0690

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