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

2013/04/02 by Andrzej Cegielski, Cegielski, Andrzej, Aviv Gibali +5
Computer Science · Mathematics · #47H05 #47H09 #47H10 #47J20 #47J40 #65K15 #90C23 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1304.0690

openalex publication_date 2013/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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