Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem formulation or is relying on a solver that automatically detects and handles symmetries. While modelers of a problem can handle various kinds of symmetries, … Read more
We consider a multistage variant of the classical stochastic capacitated facility location problem under facility disruption uncertainty. Two solution algorithms for this problem class are presented: (1) stochastic dual dynamic integer programming (SDDiP), the state-of-the-art algorithm for solving multistage stochastic integer programs, and (2) shadow price approximation (SPA), an algorithm utilizing trained parameters of the … Read more
We analyze the Douglas-Rachford splitting method for weakly convex optimization problems, by the token of the Douglas-Rachford envelope, a merit function akin to the Moreau envelope. First, we use epi-convergence techniques to show that this artifact approximates the original objective function via epigraphs. Secondly, we present how global convergence and local linear convergence rates for … Read more
The parallel processor scheduling and bin packing problems with contiguity constraints are important in the field of combinatorial optimization because both problems can be used as components of effective exact decomposition approaches for several two-dimensional packing problems. In this study, we provide an extensive review of existing mathematical formulations for the two problems, together with … Read more
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders’, (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer L-shaped cuts correspond to one of the optimal solutions of the Lagrangian dual problem, and, therefore, belong to the class of Lagrangian … Read more
Nonconvex separable piecewise linear functions (PLFs) frequently appear in applications and to approximate nonlinearitites. The standard practice to formulate nonconvex PLFs is from the perspective of discrete optimisation, using special ordered sets and mixed integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and present a spatial branch-and-bound algorithm (sBB) … Read more
Many discrete optimal control problems feature combinatorial constraints on the possible switching patterns, a common example being minimum dwell-time constraints. After discretizing to a finite time grid, for these and many similar types of constraints, it is possible to give a description of the convex hull of feasible (finite-dimensional) binary controls via extended formulations. In … Read more
Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant for any graph. The first variant uses the SDP relax- ation first to reduce the search space considerably. One … Read more
Article Download View Complexities of inexact cubic-regularized primal-dual methods for finding second-order stationary points
In this paper, we address the three-dimensional open-dimension rectangular packing problem (3D-ODRPP). This problem addresses a set of rectangular boxes of given dimensions and a rectangular container of open dimensions. The objective is to pack all boxes orthogonally into the container while minimizing the container volume. Real-world applications of the 3D-ODRPP arise in production systems … Read more