Tight Probability Bounds for Hausdorff Random Variables with Applications to Optimal Cancer Radiotherapy Treatment Design
Date
2015-09-25
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The goal of this thesis is to examine tight computable bounds on a probability measure generated by its moments. We study measures supported on a real line and propose an extension of the classical moment problem to the so-called rational moments. Specifically, we examine semidefinite and linear optimization formulations for solving the univariate rational Hausdorff moment problem given a vector of moments. We further investigate shifted moments to reduce the distance between probability bounds, and propose a numerical method to better position such shifts. In addition, when only a few raw and shifted moments are known, we derive novel extensions of the Markov and Chebyshev bounds.
Motivated by the problem of optimal radiotherapy treatment design, we present a novel and first in its class cutting plane method to be included within the mixed integer branch and cut scheme. Implementing these cuts results in as much as a 40% runtime reduction.
Description
Keywords
Mathematics
Citation
Weppler, S. (2015). Tight Probability Bounds for Hausdorff Random Variables with Applications to Optimal Cancer Radiotherapy Treatment Design (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/28449