A conjugate-gradient based approach for approximate solutions of quadratic programs
2008 (English)Report (Other academic)
This paper deals with numerical behaviour and convergence properties of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions on the columns in a column generation method is studied, and numerical results are given for quadratic programs corresponding to three patient cases. In particular, it is noted that with a bound on the two-norm of the columns, the method is equivalent to the conjugate-gradient method. Further, the above-mentioned column generation approach for radiotherapy is obtained by employing a restriction based on the infinity-norm and non-negativity. The column generation method has weak convergence properties if restricted to generating feasible step-and-shoot plans, with a "tailing-off" effect for the objective values. However, the numerical results demonstrate that, like the conjugate-gradient method, a rapid decrease of the objective value is obtained in the first few iterations. For the three patient cases, the restriction on the columns to generate feasible step-and-shoot plans has small effect on the numerical efficiency.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2008. , 14 p.
Trita-MAT. OS, ISSN 1401-2294 ; 2008:02
column generation, conjugate-gradient method, intensity-modulated radiation therapy, step-and-shoot delivery
IdentifiersURN: urn:nbn:se:kth:diva-92115OAI: oai:DiVA.org:kth-92115DiVA: diva2:512118
QC 201203262012-03-262012-03-262012-03-26Bibliographically approved