We call an optimization problem an optimization problem with controllable uncertainty if a) it contains uncertain input data and b) prior to deciding the optimization variables, the optimizer can for a certain cost reduce the scenario set of this uncertain data. In particular, we are interested in situations where each uncertain parameter is a priori … Read more
We consider a robust variant of the vehicle routing problem with heterogeneous time windows (RVRP-HTW) with a focus on delay-resistant solutions. Here, customers have different availability time windows for every vehicle and must be provided with a preferably tight appointment window for the planned service. Different vehicles are a possibility to model different days on … Read more
Due to their nested structure, bilevel problems are intrinsically hard to solve – even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. We provide an extension of the … Read more
Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more
Robust and bilevel optimization share the common feature that they involve a certain multilevel structure. Hence, although they model something rather different when used in practice, they seem to have a similar mathematical structure. In this paper, we analyze the connections between different types of robust problems (strictly robust problems with and without decision-dependence of … Read more
The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be realized in practice. A tacit assumption in this approach is that the pricing decision … Read more
Robust optimization approaches compute solutions resilient to data uncertainty, represented by a given uncertainty set. Instead, the problem of computing the largest uncertainty set that a given solution can support was, so far, quite neglected and the only results refer to the single stage framework. For that setting, it was proved that this problem can … Read more
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
\(\) 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
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