Paper Info
Title
A majorization-minimization algorithm for split feasibility problems.
Abstract
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including convex feasibility, linear complementarity, and regression with constraint sets. When a feasible point does not exist, solution methods that proceed by minimizing a proximity function can be used to obtain optimal approximate solutions to the problem. We present an extension of the proximity function approach that generalizes the linear split feasibility problem to allow for non-linear mappings. Our algorithm is based on the principle of majorization–minimization, is amenable to quasi-Newton acceleration, and comes complete with convergence guarantees under mild assumptions. Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences. We explore several examples illustrating the merits of non-linear formulations over the linear case, with a focus on optimization for intensity-modulated radiation therapy.
Year
DOI
Venue
2018
10.1007/s10589-018-0025-z
Comp. Opt. and Appl.
Keywords
Field
DocType
Majorize–minimize, Nonlinear split feasibility, Intensity modulated radiation therapy, Proximity function minimization, Constrained regression
Complementarity (molecular biology),Convergence (routing),Mathematical optimization,Range constraint,Euclidean distance,Algorithm,Regular polygon,Linear map,Inverse problem,Acceleration,Mathematics
Journal
Volume
Issue
ISSN
71
3
0926-6003
Citations 
PageRank 
References 
0
0.34
18
Authors
4
Name
Order
Citations
PageRank
jason xu111.36
Eric C. Chi2936.89
Meng Yang3102855.17
Kenneth Lange432.80