The Split Common Null Point Problem

2011/08/30 by C.L. Byrne, Charles Byrne, Byrne, Charles +6
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.FA #math.OC

paper · pdf · doi:10.48550/arxiv.1108.5953

Journal of Nonlinear and Convex Analysis, accepted for publication

openalex publication_date 2011/08/30 · arxiv created 2012/04/16 · arxiv updated 2012/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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