An Algorithm for Solving the Variational Inequality Problem Over the Fixed Point Set of a Quasi-Nonexpansive Operator in Euclidean Space

作者：Cegielski Andrzej; Gibali Aviv; Reich Simeon^*; Zalas Rafal

来源：Numerical Functional Analysis and Optimization, 2013, 34(10): 1067-1096.

DOI：10.1080/01630563.2013.771656

• Fixed point
• Quasi-nonexpansive operator
• Variational inequality problem
• 47H05
• 47H09
• 47H10
• 47J20
• 47J40
• 65K15
• 90C23

This article is concerned with the variational inequality problem VIP(F, Fix(T)): find such that for all zFix(T), where T: (nn) is quasi-nonexpansive, Fix(T) is its nonempty fixed point set, and F: (nn) is monotone. 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.

• 出版日期2013-10-3