Optimization Online


The multiple-sets split feasibility problem and its applications for inverse problems

Yair Censor (yair***at***math.haifa.ac.il)
Tommy Elfving (toelf***at***mai.liu.se)
Nirit Kopf (nirit.kopf***at***intel.com)
Thomas Bortfeld (TBORTFELD***at***PARTNERS.ORG)

Abstract: The multiple-sets split feasibility problem requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator's range. It generalizes the convex feasibility problem as well as the two-sets split feasibility problem. We propose a projection algorithm that minimizes a proximity function that measures the distance of a point from all sets. The formulation, as well as the algorithm, generalize earlier work on the split feasibility problem. We offer also a generalization to proximity functions with Bregman distances. Application of the method to the inverse problem of intensity-modulated radiation therapy (IMRT) treatment planning is studied in a separate companion paper and is here only briefly described.

Keywords: Multiple-sets split feasibility; proximity function; Bregman projections; inverse problems; intensity-modulated radiation therapy.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering

Category 3: Applications -- Science and Engineering (Biomedical Applications )

Citation: Inverse Problems, Vol. 21 (2005), pp. 2071-2084.


Entry Submitted: 11/22/2005
Entry Accepted: 11/25/2005
Entry Last Modified: 11/25/2005

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society