General Polyhedral Approximation of Two-Stage Robust Linear Programming

\(\) We consider two-stage robust linear programs with a budget of uncertainty for the righthand side. In this scenario set, which is frequently used in robust optimization, the uncertain righthand side for each row lies in an interval and the relative increases summed over all rows are less than a budget \(\Gamma\). We develop a … Read more

On the Relation Between Affinely Adjustable Robust Linear Complementarity and Mixed-Integer Linear Feasibility Problems

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

Target-Oriented Regret Minimization for Satisficing Monopolists

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

Robust Contextual Portfolio Optimization with Gaussian Mixture Models

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

Hidden convexity in a class of optimization problems with bilinear terms

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

The Analytics of Robust Satisficing

We propose a new prescriptive analytics model based on robust satisficing that incorporates a prediction model to determine the here-and-now decision that would achieve a target expected reward as well as possible under both risk ambiguity and estimation uncertainty. The reward function of the decision model depends on some observable parameters whose future realizations are … Read more

Robust Optimization with Continuous Decision-Dependent Uncertainty

We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU). RO-CDDU has two main features that have not been addressed in the literature: an uncertainty set with linear dependence on continuous decision variables and a convex piecewise-linear objective function. We prove that RO-CDDU is NP-hard in general. To address the computational challenges, we reformulate … Read more

Robust Phi-Divergence MDPs

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

Robust Explainable Prescriptive Analytics

We propose a new robust explainable prescriptive analytics framework that minimizes a risk-based objective function under distributional ambiguity by leveraging the data collected on the past realizations of the uncertain parameters affecting the decision model and the side information that have some predictive power on those uncertainties. The framework solves for an explainable response policy … Read more

Two-Stage Robust Optimization with Decision Dependent Uncertainty

The type of decision dependent uncertainties (DDUs) imposes a great challenge in decision making, while existing methodologies are not sufficient to support many real practices. In this paper, we present a systematic study to handle this challenge in two-stage robust optimization~(RO). Our main contributions include three sophisticated variants of column-and-constraint generation method to exactly compute … Read more