相关论文: Computing Convex Hulls with a Linear Solver

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…

An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…

Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…

In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two points of the configuration (where the lines are generated…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

We present a formalization of convex polyhedra in the proof assistant Coq. The cornerstone of our work is a complete implementation of the simplex method, together with the proof of its correctness and termination. This allows us to define…

Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and in some cases more efficient than LP, CLP or LP + tabling. Previous designs of TCLP systems did not fully…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

Constraint Handling Rules (CHR) is a declarative committed-choice programming language with a strong relationship to linear logic. Its generalization CHR with Disjunction (CHRv) is a multi-paradigm declarative programming language that…

Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…

We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…

Probabilistic Programming Languages (PPLs) are a powerful tool in machine learning, allowing highly expressive generative models to be expressed succinctly. They couple complex inference algorithms, implemented by the language, with an…

We introduce a natural notion of depth that applies to individual cutting planes as well as entire families. This depth has nice properties that make it easy to work with theoretically, and we argue that it is a good proxy for the practical…

It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…

This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time.…

The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…

We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible…

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…