This paper considers the problem of computing the non-causal minimum-fuel energy management strategy of a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem arising when optimal gear choice, torque split and engine on/off controls are sought in off-line evaluations. We propose an efficient model by … Read more
Recently, Kronqvist et al.rediscovered the supporting hyperplane algorithm of Veinott and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm applied to a particular … Read more
We consider a linear regression model for which we assume that many of the observed regressors are irrelevant for the prediction. To avoid overfitting, we conduct a variable selection and only include the true predictors for the least square fitting. The best subset selection gained much interest in recent years for addressing this objective. For … Read more
One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over … Read more
Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, etc. Often, these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization one develops primal heuristics in order to obtain … Read more
This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more
Circle packing problems are a class of packing problems which attempt to pack a given set of circles into a container with no overlap. In this paper, we focus on the circle packing problem proposed by L{\’o}pez et.al. The problem is to pack circles of unequal size into a fixed size circular container, so as … Read more
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an L0 constraint restricting the support of the estimators is a challenging non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based … Read more
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and … Read more
We present a framework to obtain valid inequalities for optimization problems constrained by a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are particularly interested in cases where the closure of the convex set is either non-polyhedral, or is defined … Read more