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Weak and Strong Convergence of Algorithms for 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 space. 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, accepted for publication, DOI 10.1007/s11075-011-9490-5]. 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 three iterative algorithms that solve such problems in Hilbert space, and establish weak convergence for one and strong convergence for the other two.

Keywords:

Category 1: Complementarity and Variational Inequalities

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Nonlinear Optimization

Citation: Technical Report, August 29, 2011.

Download: [PDF]

Entry Submitted: 08/30/2011
Entry Accepted: 08/30/2011
Entry Last Modified: 08/30/2011

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