Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve – both in theory and practice. Fortunately, there have been significant algorithmic advances in the field so that we can solve much larger and also more complicated problems today compared to what was possible to … Read more
\(\) We consider two-stage robust linear programs with uncertain righthand side. We develop a General Polyhedral Approximation (GPA), in which the uncertainty set $\mathcal{U}$ is substituted by a finite set of polytopes derived from the vertex set of an arbitrary polytope that dominates $\mathcal{U}$. The union of the polytopes need not contain $\mathcal{U}$. We analyse … Read more
We consider adjustable robust linear complementarity problems and extend the results of Biefel et al.~(2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a given linear complementarity problem is equivalent to solving a properly chosen mixed-integer linear feasibility problem. Article … Read more
We study a robust monopoly pricing problem where a seller aspires to sell an item to a buyer. We assume that the seller, unaware of the buyer’s willingness to pay, ambitiously optimizes over a space of all individual rational and incentive compatible mechanisms with a regret-type objective criterion. Using robust optimization, Kocyigit et al. (2021) … Read more
We consider the portfolio optimization problem with contextual information that is available to better quantify and predict the uncertain returns of assets. Motivated by the regime modeling techniques for the finance market, we consider the setting where both the uncertain returns and the contextual information follow a Gaussian Mixture (GM) distribution. This problem is shown … Read more
In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. A reformulation technique is presented which converts the problems in this class … Read more
We introduce a novel approach to prescriptive analytics that leverages robust satisficing techniques to determine optimal decisions in situations of risk ambiguity and prediction uncertainty. Our decision model relies on a reward function that incorporates uncertain parameters, which can be partially predicted using available side information. However, the accuracy of the linear prediction model depends … Read more
We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU), which has two new features: an uncertainty set linearly dependent on continuous decision variables and a convex piecewise-linear objective function. We prove that RO-CDDU is strongly NP-hard in general and reformulate it into an equivalent mixed-integer nonlinear program (MINLP) with a decomposable structure to … Read more
In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view … Read more
We propose a new robust actionable prescriptive analytics framework that leverages past data and side information to minimize a risk-based objective function under distributional ambiguity. Our framework aims to find a policy that directly transforms the side information into implementable decisions. Specifically, we focus on developing actionable response policies that offer the benefits of interpretability … Read more