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The Split Common Null Point Problem

Charles Byrne(Charles_Byrne***at***uml.edu)
Yair Censor(yair***at***math.haifa.ac.il)
Aviv Gibali(avivg***at***techunix.technion.ac.il)
Simeon Reich(sreich***at***techunix.technion.ac.il)

Abstract: We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert spaces. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms 59 (2012), 301--323]. The SCNPP with only two set-valued mappings entails finding a zero of a maximal monotone mapping in one space, the image of which under a given bounded linear transformation is a zero of another maximal monotone mapping. We present four iterative algorithms that solve such problems in Hilbert spaces, and establish weak convergence for one and strong convergence for the other three.

Keywords:

Category 1: Complementarity and Variational Inequalities

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Journal of Nonlinear and Convex Analysis , accepted for publication.

Download: [PDF]

Entry Submitted: 04/16/2012
Entry Accepted: 04/16/2012
Entry Last Modified: 04/16/2012

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