相关论文: Computing Convex Hulls with a Linear Solver

We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…

We consider the problem of the computation of $\inf_p \theta p$ over the set of exponent pairs $P \ni p$ under linear constraints for a certain class of objective functions $\theta$. An effective algorithm is presented. The output of the…

We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the…

In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…

We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…

Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…

The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…

We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…

We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations,…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

In this paper we derive strong linear inequalities for sets of the form {(x, q) \in Rd \times R : q \geq Q(x), x \in Rd - int(P)}, where Q(x) : Rd \rightarrow R is a quadratic function, P \subset Rd and "int" denotes interior. Of particular…

We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…

In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points…

As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…