Optimization Online


Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

Mark Brooke(mark.brooke***at***oncology.ox.ac.uk)
Yair Censor(yair***at***math.haifa.ac.il)
Aviv Gibali(avivg***at***braude.ac.il)

Abstract: In this paper we study a feasibility-seeking problem with percentage violation con- straints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a speci ed fraction of the number of constraints in each subset is allowed to be violated by up to a speci ed percentage of the existing bounds. Our motiva- tion to investigate problems with percentage violation constraints comes from the eld of radiation therapy treatment planning wherein the fully-discretized inverse planning problem is formulated as a split feasibility problem and the percentage violation con- straints give rise to non-convex constraints. We develop a string-averaging CQ method that uses only projections onto the individual sets which are half-spaces represented by linear inequalities. The question of extending our theoretical results to the non- convex sets case is still open. We describe how our results apply to radiation therapy treatment planning.

Keywords: String-averaging, CQ-algorithm, split feasibility, percentage violation con- straints, radiation therapy treatment planning, dose-volume constraints, common xed points, inverse problem, Landweber operator, cutter operator.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

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

Citation: Preprint, November 2019.

Download: [PDF]

Entry Submitted: 11/26/2019
Entry Accepted: 11/26/2019
Entry Last Modified: 11/26/2019

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 Optimization Society