We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main … Read more
In this paper, we present a method to determine if a lift-and-project cut for a mixed-integer linear program is regular, in which case the cut is equivalent to an intersection cut from some basis of the linear relaxation. This is an important question due to the intense research activity for the past decade on cuts … Read more
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and nonsmooth functions while the outer one is the minimization … Read more
A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows that the Lipschitz assumption is unnecessary when the forward steps are performed in finite-dimensional spaces: a backtracking linesearch … Read more
Recent papers indicate that some algorithms for constrained optimization may exhibit worst-case complexity bounds that are very similar to those of unconstrained optimization algorithms. A natural question is whether well established practical algorithms, perhaps with small variations, may enjoy analogous complexity results. In the present paper we show that the answer is positive with respect … Read more
The primary focus of this paper is on designing inexact first-order methods for solving large-scale constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the computational cost needed for each iteration. A penalty parameter updating strategy during the subproblem solve enables the algorithm to automatically detect infeasibility. Global … Read more
Modeling time-varying operations in complex energy systems optimization problems is often computationally intractable, and time-series input data are thus often aggregated to representative periods. In this work, we introduce a framework for using clustering methods for this purpose, and we compare both conventionally-used methods (k-means, k-medoids, and hierarchical clustering), and shape-based clustering methods (dynamic time … Read more
We examine the robust counterpart of the classical Capacitated Vehicle Routing Problem (CVRP). We consider two types of uncertainty sets for the customer demands: the classical budget polytope introduced by Bertsimas and Sim (2003), and a partitioned budget polytope proposed by Gounaris et al. (2013). We show that using the set-partitioning formulation it is possible … Read more
We examine an extension of the Traveling Salesperson Problem (TSP), the so called TSP with Forbidden Neighborhoods (TSPFN). The TSPFN is asking for a shortest Hamiltonian cycle of a given graph, where vertices traversed successively have a distance larger than a given radius. This problem is motivated by an application in mechanical engineering, more precisely … Read more
In this paper we investigate the Locomotive Scheduling Problem, i.e., the optimization of locomotive utilization with prior known transports that must be performed. Since railway timetables are typically planned a year in advance, the aim is to assign locomotives to trains such that the locomotive utilization is maximized while maintenance constraints are taken into account. … Read more