Robust approaches for optimization problems with convex uncertainty

Abstract

This thesis discusses different methods for robust optimization problems that are convex in the uncertain parameters. Such problems are inherently difficult to solve as they implicitly require the maximization of convex functions. First, an approximation of such a robust optimization problem based on a reformulation to an equivalent adjustable robust linear optimization problem is proposed. Then, an algorithm to solve convex maximization problems is developed that can be used in a cutting-set method for robust convex problems. Last, distributionally robust optimization is explored as an alternative approach to deal with this convexity. Specifically, it is applied to a novel problem formulation to reduce conservatism in robust optimization and project planning. Additionally, a new tail probability bound is derived that can be used for distribution-free analysis of many OR problems.