We deal with a recently proposed method of Chubanov [1] for solving linear homogeneous systems with positive variables. Some improvements of Chubanov’s method and its analysis are presented. We propose a new and simple cut criterion and show that the cuts defined by the new criterion are at least as sharp as in [1]. The … Read more
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The … Read more
We show how random projections can be used to solve large-scale dense linear programs approximately. This is a new application of techniques which are now fairly well known in probabilistic algorithms, but have never yet been systematically applied to the fundamental class of Linear Programming. We develop the necessary theoretical framework, and show that this … Read more
Electronic structure calculations, in particular the computation of the ground state energy, lead to challenging problems in optimization. These problems are of enormous importance in quantum chemistry for calculations of properties of solids and molecules. Minimization methods for computing the ground state energy can be developed by employing a variational approach, where the second-order reduced … Read more
Crashing is a method for optimally shortening the project makespan by reducing the time of one or more activities in a project network by allocating resources to it. Activity durations are however uncertain and techniques in stochastic optimization, robust optimization and distributionally robust optimization have been developed to tackle this problem. In this paper, we … Read more
Recently, Chubanov proposed an interesting new polynomial-time algorithm for linear program. In this paper, we extend his algorithm to second-order cone programming. ArticleDownload View PDF
This document briefly describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required. ArticleDownload View PDF
In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem … Read more
We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization problem. We extend our prior work on disjunctive conic cuts, which has thus far been restricted to the case in which the intersection of the hyperplanes and … Read more
We use moment methods to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate the infinite dimensional optimization problems in this hierarchy by block diagonal semidefinite programs. For this we develop the necessary harmonic analysis for spaces consisting of subsets of another space, and … Read more