We present a mixed-integer optimization (MIO) approach to sparse Poisson regression. The MIO approach to sparse linear regression was first proposed in the 1970s, but has recently received renewed attention due to advances in optimization algorithms and computer hardware. In contrast to many sparse estimation algorithms, the MIO approach has the advantage of finding the … Read more
The Steiner tree problem in graphs (SPG) is one of the most studied problems in combinatorial optimization. In the last 10 years, there have been significant advances concerning approximation and complexity of the SPG. However, the state of the art in (practical) exact solution of the SPG has remained largely unchallenged for almost 20 years. … Read more
Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull. In this paper we experimentally investigate the dimensions of faces induced by general-purpose cutting planes generated by a state-of-the-art solver. Therefore, we relate … Read more
We study representation of solutions and certificates to quadratic and cubic optimization problems. Specifically, we focus on minimizing a cubic function over a polyhedron and also minimizing a linear function over quadratic constraints. We show when there exist rational feasible solutions (and if we can detect them) and when we can prove feasibility of sublevel … Read more
We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus we introduce and study the structure of a totally-ordered multiple knapsack set. The valid multi-cover inequalities we derive for its convex hull have … Read more
We study the inefficiency of pure Nash equilibria in symmetric network congestion games defined over series-parallel networks with affine edge delays. For arbitrary networks, Correa (2019) proved a tight upper bound of 5/2 on the PoA. On the other hand, for extension-parallel networks, a subclass of series-parallel networks, Fotakis (2010) proved that the PoA is … Read more
This paper shows that there exists a Nash equilibrium of an n-player chance-constrained game for elliptically symmetric distributions. For a certain class of payoff functions, we suitably construct an equivalent mathematical program whose global maximizer is a Nash equilibrium. ArticleDownload View PDF
This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose … Read more
Drone delivery is drawing increasing attention in last-mile delivery. Effective solution methods to solve decision-making problems arising in drone delivery allow to run and assess drone delivery systems. In this paper, we focus on delivery systems with a single traditional vehicle and multiple drones working in tandem to fulfill customer requests. We address the Traveling … Read more
The running time for solving a mixed-integer linear optimization problem (MIP) strongly depends on the number of its integral variables. Bader et al. [Math. Progr. 169 (2018) 565–584] equivalently reformulate an integer program into an MIP that contains a reduced number of integrality constraints, when compared to the original model. Generalizing the concept of totally … Read more