The document describes COIN-OR METSlib, a C++ framework for local search based metaheuristics. METSlib has been used to implement a massively parallel VRP algorithm, a state of the art Vertex Coloring Problem solver, a Timetabling software, and in many other projects. ArticleDownload View PDF
A closed convex cone K is called nice, if the set K^* + F^\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\perp is the orthogonal complement of the linear span of F. The niceness property plays a role in the facial reduction algorithm of Borwein … Read more
We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing theory. … Read more
This paper introduces the PuLP library, an open source package that allows mathematical programs to be described in the Python computer programming language. PuLP is a high-level modelling library that leverages the power of the Python language and allows the user to create programs using expressions that are natural to the Python language, avoiding special … Read more
We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems, and establish … Read more
Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim (2004). We present three different mathematical formulations for this problem, provide valid inequalities, … Read more
In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (2008). By analyzing $n$-dimensional lattice-free sets, we prove that for every integer $n$ there exists a positive integer $t$ such that every facet-defining inequality of the … Read more
We prove that any minimal valid function for the k-dimensional infinite group relaxation that is piecewise linear with at most k+1 slopes and does not factor through a linear map with non-trivial kernel is extreme. This generalizes a theorem of Gomory and Johnson for k=1, and Cornu\’ejols and Molinaro for k=2. ArticleDownload View PDF
This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are … Read more
The perceptron algorithm, introduced in the late fifties in the machine learning community, is a simple greedy algorithm for finding a solution to a finite set of linear inequalities. The algorithm’s main advantages are its simplicity and noise tolerance. The algorithm’s main disadvantage is its slow convergence rate. We propose a modified version of the … Read more