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
\(\) We analyze the inverse of integer programs (IPs) using the Gomory corner relaxation (GCR). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We propose a linear program formulation for the inverse GCR under \(L_1\) and \(L_\infty\) norms.The inverse … Read more
Article Download View Quantum Annealing for the two-level Facility Location Problem
Article Download View Stochastic approximation algorithms for DR-submodular maximization with convex functional constraints
In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for unconstrained and linearly constrained problems. In particular, when minimizing a function with $n$ variables, we prove that at most ${\cal O}(n\epsilon^{-2})$ iterations are needed to … Read more