p-Cone Optimization with Application to Radiotherapy Planning

Date
2015-10-07
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The work presented in this thesis is dedicated to the study of two facets of the so-called p-cone optimization: one methodological and mostly theoretical, while the other applied and computational. Motivated by optimal radiotherapy design for cancer treatment, we investigate the computational hardness of p-cone optimization, namely the complexity of forming a tractable approximation to such a problem, as well as the suitability of p-cone optimization to optimal radiotherapy design. It is demonstrated by Ben-Tal and Nemirovski that an ε-approximation to a Second Order Conic Optimization (SOCO) problem is polynomial reducible to Linear Optimization (LO). In this thesis, we consider a generalization of SOCO to p-Order Conic Optimization (pOCO) where the second order cone is replaced with the p-norm cone. In the first part of the thesis, we develop three conic approximation schemes for p-norm cone and estimate their complexities. We proposed a second order conic approximation with complexity of O(4√1/ε) on the number of affine inequalities giving ε cone approximation. In the second part of the thesis, a novel unconstrained convex moment based model is proposed to enable embedding of so-called dose volume histogram in the context of radiation therapy planning optimization. We investigate the suitability of the newly proposed method and compare its performance to other three known methods to replicate a set of dose volume histograms. We provide a benchmark of performance of each method in terms of dosimetery and run time.
Description
Keywords
Biophysics--Medical, Mathematics
Citation
Shirvani Ghomi, P. (2015). p-Cone Optimization with Application to Radiotherapy Planning (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27279