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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

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