Robust optimization: from the uncertainty set to the solution and back

So far, robust optimization have focused on computing solutions resilient to data uncertainty, given an uncertainty set representing the possible realizations of this uncertainty. Here, instead, we are interested in answering the following question: once a solution of a problem is given, which is the largest uncertainty set that this solution can support? We address … Read more

Safely Learning Dynamical Systems

\(\) A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the … Read more

A Moment-SOS Hierarchy for Robust Polynomial Matrix Inequality Optimization with SOS-Convexity

We study a class of polynomial optimization problems with a robust polynomial matrix inequality constraint for which the uncertainty set is defined also by a polynomial matrix inequality (including robust polynomial semidefinite programs as a special case). Under certain SOS-convexity assumptions, we construct a hierarchy of moment-SOS relaxations for this problem to obtain convergent upper … Read more

Robust optimal design of a tree-based water distribution network with intermittent demand

This paper discusses the design of a tree-shaped water distribution system for small, dispersed rural communities. It revisits the topic that was discussed in [Babonneau et al., 2019] and is nowadays implemented in the field. It proposes a new approach to pipe selection based on robust optimization to account for the uncertainty inherent in intermittent … Read more

Finding Regions of Counterfactual Explanations via Robust Optimization

Counterfactual explanations play an important role in detecting bias and improving the explainability of data-driven classification models. A counterfactual explanation (CE) is a minimal perturbed data point for which the decision of the model changes. Most of the existing methods can only provide one CE, which may not be achievable for the user. In this … Read more

Multi-Stage Robust Mixed-Integer Programming

Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more

Optimality-Based Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs

We use sensitivity analysis to design optimality-based discretization (cutting-plane) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal discretization of SIPs as a max-min problem and propose variants that are more computationally tractable. We then use parametric sensitivity theory to design an efficient method for solving these max-min … Read more

Robust Two-Dose Vaccination Schemes and the Directed b-Matching Problem

In light of the recent pandemic and the shortage of vaccinations during their roll-out, questions arose regarding the best strategy to achieve immunity throughout the population by adjusting the time gap between the two necessary vaccination doses. This strategy has already been studied from different angles by various researches. However, the deliveries of vaccination doses … Read more

Approximation Algorithms for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It … Read more

Two-stage and Lagrangian Dual Decision Rules for Multistage Adaptive Robust Optimization

In this work, we design primal and dual bounding methods for multistage adjustable robust optimization (MSARO) problems by adapting two decision rules rooted in the stochastic programming literature. This approach approximates the primal and dual formulations of an MSARO problem with two-stage models. From the primal perspective, this is achieved by applying two-stage decision rules … Read more