Related papers: Computing Convex Hulls with a Linear Solver
Number Decision Diagrams (NDD) provide a natural finite symbolic representation for regular set of integer vectors encoded as strings of digit vectors (least or most significant digit first). The convex hull of the set of vectors…
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…
We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…
We study the complexity of computing the mixed-integer hull $\operatorname{conv}(P\cap\mathbb{Z}^n\times\mathbb{R}^d)$ of a polyhedron $P$. Given an inequality description, with one integer variable, the mixed-integer hull can have…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
A new line clipping algorithm against convex polyhedron in E3 with an expected complexity O(1) is presented. The suggested approach is based on two orthogonal projections to E2 co-ordinate system and on pre-processing of the given…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
We study the following range searching problem: Preprocess a set $P$ of $n$ points in the plane with respect to a set $\mathcal{O}$ of $k$ orientations % , for a constant, in the plane so that given an $\mathcal{O}$-oriented convex polygon…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
In this paper we look for the convex hull of a set using the geometric evolution by minimal curvature of a hypersurface that surrounds the set. To find the convex hull, we study the large time behavior of solutions to an obstacle problem…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We study a natural extension to the well-known convex hull problem by introducing multiplicity: if we are given a set of convex polygons, and we are allowed to partition the set into multiple components and take the convex hull of each…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited…