Work

The Split Common Null Point Problem

Year: 2011

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1108.5953

Authors: Byrne, Charles, Censor, Yair, Gibali, Aviv, Reich, Simeon

Institutions: University of Massachusetts Lowell, University of Haifa, Technion – Israel Institute of Technology

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: United States-Israel Binational Science Foundation, Israel Science Foundation

Award: G3892099302

OpenAlex ID: W2140063001

Cites: 42

Cited by: 171

Related to: 20