Related papers: Computing Convex Hulls with a Linear Solver

Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…

Let V be a semialgebraic set parameterized by quadratic polynomials over a quadratic set T. This paper studies semidefinite representation of its convex hull by projections of spectrahedra (defined by linear matrix inequalities). When T is…

The convex hull of a set of points, $C$, serves to expose extremal properties of $C$ and can help identify elements in $C$ of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be…

Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…

This paper proposes an evaluation of the adequacy of the constraint logic programming paradigm for natural language processing. Theoretical aspects of this question have been discussed in several works. We adopt here a pragmatic point of…

We describe a pure divide-and-conquer parallel algorithm for computing 3D convex hulls. We implement that algorithm on GPU hardware, and find a significant speedup over comparable CPU implementations.

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…

A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

This paper evaluates several improvements to the memory layout of convex hulls to improve computation times for support point queries. The support point query is a fundamental part of common collision algorithms, and the work presented…

The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

We present Epsilon, a system for general convex programming using fast linear and proximal operators. As with existing convex programming frameworks, users specify convex optimization problems using a natural grammar for mathematical…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…

Suppose $<A_i, \vec{c}_i>$ are planar (convex) H-polyhedra, that is, $A_i \in \mathbb{R}^{n_i \times 2}$ and $\vec{c}_i \in \mathbb{R}^{n_i}$. Let $P_i = \{\vec{x} \in \mathbb{R}^2 \mid A_i\vec{x} \leq \vec{c}_i \}$ and $n = n_1 + n_2$. We…

Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many…

A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…