The deepest event cuts in risk-averse optimization with application to radiation therapy design

Our study is motivated by radiation therapy design for cancer treatment. We consider large-scale problems with stochastic order constraints. We establish a general result about the form of the deepest cuts associated with events of positive probability which are used in the numerical approximation of the functional constraints. An efficient method using the deepest cuts is proposed for the numerical solution of problems with second-order dominance constraints and increasing convex order constraints. We the propose a new methodology for the radiation-therapy design for cancer treatment. We introduce a risk-averse optimization problem with two types of stochastic order relations and with coherent measures of risk and consider the effect of the risk models in three versions of the problem formulation. Additionally, we propose a method that creates flexible (floating) benchmark distributions when benchmark distributions are not given apriori or when the provided distributions lead to infeasibility. We devise a numerical method using floating benchmarks for solving the proposed risk-averse optimization models for radiation therapy design. The models and methods are verified by using clinical data confirming the viability of the proposed methodology and its efficiency.