Piecewise Polyhedral Relaxations of Multilinear Optimization

In this paper, we consider piecewise polyhedral relaxations (PPRs) of multilinear optimization problems over axis-parallel hyper-rectangular partitions of their domain. We improve formulations for PPRs by linking components that are commonly modeled independently in the literature. Numerical experiments with ALPINE, an open-source software for global optimization that relies on piecewise approximations of functions, show that … Read more

A Stochastic Optimization Approach to Energy-Efficient Underground Timetabling under Uncertain Dwell and Running Times

We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy-efficiency of a timetable. Since deviations from a planned timetable … Read more

Multi-Echelon Inventory Management for a Non-Stationary Capacitated Distribution Network

We present an inventory management solution for a non-stationary capacitated multi-echelon distribution network involving thousands of products. Assuming backlogged sales, we revisit and leverage the seminal multi-echelon inventory management results in the literature to establish the structural properties of the problem, and derive an efficient and practical solution method. In particular, we describe how the … Read more

Hidden convexity in a class of optimization problems with bilinear terms

In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. A reformulation technique is presented which converts the problems in this class … Read more

Using Neural Networks to Solve Linear Bilevel Problems with Unknown Lower Level

Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower’s problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower’s problem is not explicitly known by the leader. For such bilevel problems … Read more