ART3+
A fast algorithm for solving a linear feasibility problem with application to intensity-modulated radiation therapy. The goal of intensity-modulated radiation therapy (IMRT) is to deliver sufficient doses to tumors to kill them, but without causing irreparable damage to critical organs. This requirement can be formulated as a linear feasibility problem. The sequential (i.e., iteratively treating the constraints one after another in a cyclic fashion) algorithm ART3 is known to find a solution to such problems in a finite number of steps, provided that the feasible region is full dimensional. We present a faster algorithm, called ART3+. The idea of ART3+ is to avoid unnecessary checks on constraints that are likely to be satisfied. The superior performance of the new algorithm is demonstrated by mathematical experiments inspired by the IMRT application.
Keywords for this software
References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
Sorted by year (- Dao, Minh N.; Phan, Hung M.: Linear convergence of projection algorithms (2019)
- Necoara, Ion; Richtárik, Peter; Patrascu, Andrei: Randomized projection methods for convex feasibility: conditioning and convergence rates (2019)
- Gibali, Aviv; Küfer, Karl-Heinz; Reem, Daniel; Süss, Philipp: A generalized projection-based scheme for solving convex constrained optimization problems (2018)
- Lu, Nan; Ma, Feng; Liu, Sanyang: A non-interior continuation algorithm for solving the convex feasibility problem (2014)
- Oliveira, Paulo Roberto: A strongly polynomial-time algorithm for the strict homogeneous linear-inequality feasibility problem (2014)
- Censor, Yair; Chen, Wei; Combettes, Patrick L.; Davidi, Ran; Herman, Gabor T.: On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints (2012)
- Censor, Yair; Chen, Wei; Pajoohesh, Homeira: Finite convergence of a subgradient projections method with expanding controls (2011)
- Davidi, R.; Herman, G. T.; Censor, Y.: Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections (2009)
- Herman, Gabor T.; Chen, Wei: A fast algorithm for solving a linear feasibility problem with application to intensity-modulated radiation therapy (2008)