Related papers: Computing Convex Hulls with a Linear Solver
The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…
We present new iterative algorithms for solving a square linear system $Ax=b$ in dimension $n$ by employing the {\it Triangle Algorithm} \cite{kal12}, a fully polynomial-time approximation scheme for testing if the convex hull of a finite…
Slicing is a program analysis technique originally developed for imperative languages. It facilitates understanding of data flow and debugging. This paper discusses slicing of Constraint Logic Programs. Constraint Logic Programming (CLP) is…
A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case where one…
The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…
The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…
Computationally efficient and automated generation of convex hulls is desirable for high throughput materials discovery of thermodynamically stable multi-species crystal structures. A convex hull genetic algorithm is proposed that uses…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…
Numerical tools for constraints solving are a cornerstone to control verification problems. This is evident by the plethora of research that uses tools like linear and convex programming for the design of control systems. Nevertheless, the…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
Refinements of the worst case complexity over instances of fixed input size consider the input order or the input structure, but rarely both at the same time. Barbay et al. [2016] described ``synergistic'' solutions on multisets, which take…
Given a nonlinear, univariate, bounded, and differentiable function $f(x)$, this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of $f(x)$ and its…
We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm DDM Cuts is based on the Gomory cuts and the dynamic…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…