Related papers: Intersection cuts from multiple rows: a disjunctiv…
We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…
The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (single-conclusion) cuts yield trees, which underlie ordinary natural…
In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from…
We briefly describe a new general algorithm for carrying out QCD calculations to next-to-leading order in perturbation theory. The algorithm can be used for computing arbitrary jet cross sections in arbitrary processes and can be…
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its…
Two-stage stochastic mixed-integer linear programs with mixed-integer recourse arise in many practical applications but are computationally challenging due to their large size and the presence of integer decisions in both stages. The…
We study the mixed-integer quadratic programming formulation of an $n$-period hybrid control problem with a convex quadratic cost function and linear dynamics. We first give the convex hull description of the single-period, two-mode problem…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…
The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
Schur's $Q$-functions with reduced variables are discussed by employing a combinatorics of strict partitions. They are called reduced $Q$-functions. We give a description of the linear relations among reduced $Q$-functions.
The article proposes a new method for finding the triangle-triangle intersection in 3D space, based on the use of computer graphics algorithms -- cutting off segments on the plane when moving and rotating the beginning of the coordinate…
In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring…
This paper studies bilevel polynomial optimization in which lower-level constraint functions depend linearly on lower-level variables. We show that such bilevel program can be reformulated as a disjunctive program by using…
Recently, many studies have been devoted to finding diverse solutions in classical combinatorial problems, such as Vertex Cover (Baste et al., IJCAI'20), Matching (Fomin et al., ISAAC'20) and Spanning Tree (Hanaka et al., AAAI'21). We…
In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…