Analysis on Newton projection method for the split feasibility problem

Biao Qu (), Changyu Wang () and Naihua Xiu ()
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Biao Qu: Qufu Normal University
Changyu Wang: Qufu Normal University
Naihua Xiu: Beijing Jiaotong University

Computational Optimization and Applications, 2017, vol. 67, issue 1, No 7, 175-199

Abstract: Abstract In this paper, based on a merit function of the split feasibility problem (SFP), we present a Newton projection method for solving it and analyze the convergence properties of the method. The merit function is differentiable and convex. But its gradient is a linear composite function of the projection operator, so it is nonsmooth in general. We prove that the sequence of iterates converges globally to a solution of the SFP as long as the regularization parameter matrix in the algorithm is chosen properly. Especially, under some local assumptions which are necessary for the case where the projection operator is nonsmooth, we prove that the sequence of iterates generated by the algorithm superlinearly converges to a regular solution of the SFP. Finally, some numerical results are presented.

Keywords: The split feasibility problem; Projection operator; Generalized Jacobian; Newton projection method; Global convergence and convergence rate; 90C30; 90C90; 65K05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-016-9884-3

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