\(\) We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important generalization of the Matrix Completion problem, a central problem in Statistics, Operations Research and Machine Learning, that … Read more
Empirical risk minimization often fails to provide robustness against adversarial attacks in test data, causing poor out-of-sample performance. Adversarially robust optimization (ARO) has thus emerged as the de facto standard for obtaining models that hedge against such attacks. However, while these models are robust against adversarial attacks, they tend to suffer severely from overfitting. To … Read more
We study decision problems under uncertainty, where the decision-maker has access to K data sources that carry biased information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the K data-generating distributions with respect to an optimal transport (OT) distance. In this situation the decision-maker can … Read more
In this paper, we study a distributionally robust optimization approach to chance-constrained stochastic programs to hedge against uncertainty in the distributions of the random parameters. We consider a general polyhedral ambiguity set under finite support and study Wasserstein ambiguity set, total variation distance ambiguity set, and moment-based ambiguity set as examples for our computations. We … Read more
Expected-value-constrained programming (ECP) formulations are a broad class of stochastic programming problems including integrated chance constraints, risk models, and stochastic dominance formulations. Given the wide availability of data, it is common in applications to have independent contextual information associated with the target or dependent random variables of the problem. We show how to incorporate such … Read more
We consider a two-stage stochastic program with continuous recourse, where the distribution of the random parameters depends on the decisions. Assuming a finite sample space, we study a distributionally robust approach to this problem, where the decision-dependent distributional ambiguity is modeled with a polyhedral ambiguity set. We consider cases where the recourse function and the … Read more
We consider the household assignment problem as it occurs in the geo-referencing step of spatial microsimulation models. The resulting model is a maximum weight matching problem with additional side constraints. For real-world instances such as the one for the city of Trier in Germany, the number of binary variables exceeds 10^9, and the resulting instances … Read more
Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sos-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sos-hierarchy is hereby used to solve those … Read more
In this report, we present the BOBILib, a collection of more than 2500~instances of mixed integer linear bilevel optimization problems. The goal of this library is to make a large and well-curated set of test instances freely available for the research community so that new and existing algorithms in bilevel optimization can be tested and … Read more
In the context of mixed-integer nonlinear problems (MINLPs), it is well-known that strong duality does not hold in general if the standard Lagrangian dual is used. Hence, we consider the augmented Lagrangian dual (ALD), which adds a nonlinear penalty function to the classic Lagrangian function. For this setup, we study conditions under which the ALD … Read more