We consider the solution of Mixed Integer Nonlinear Programming (MINLP) problems by a parallel implementation of nonlinear branch-and-bound on a computational grid or meta-computer. Computational experience on a set of large MINLPs is reported which indicates that this approach is efficient for the solution of large MINLPs. CitationNumerical Analysis Report NA/200, Department of Mathematics, University … Read more
The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In this paper we show how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities … Read more
We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a “ring”) does not exceed a given length K. We present here a new formulation of the problem and derive facet results for different classes … Read more
A set $S$ of vertices in a digraph $D=(V,A)$ is a kernel if $S$ is independent and every vertex in $V-S$ has an out-neighbour in $S$. We show that there exists an $O(3^{\delta \sqrt{k}} n)$~% \footnote{Throughout this paper the constants $\delta$ and $c$ are the same as the comparative constants mentioned in~\cite{kn:alber}.} algorithm to check … Read more
Until recently, the study of interior point methods has dominated algorithmic research in semidefinite programming (SDP). From a theoretical point of view, these interior point methods offer everything one can hope for; they apply to all SDP’s, exploit second order information and offer polynomial time complexity. Still for practical applications with many constraints $k$, the … Read more
This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data. CitationRapport de recherche 4179, INRIA, France, 2001ArticleDownload View PDF
We propose and describe a hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP+PR) for the Steiner problem in graphs. In this multi-start approach, the greedy randomized construction phase of a GRASP is replaced by the use of several construction heuristics with a weight perturbation strategy that combines intensification and diversification elements, as in … Read more
Parallel implementations of metaheuristics appear quite naturally as an effective alternative to speed up the search for approximate solutions of combinatorial optimization problems. They not only allow solving larger problems or finding improved solutions with respect to their sequential counterparts, but they also lead to more robust algorithms. We review some trends in parallel computing … Read more
In this paper we consider the labor constrained scheduling problem (LCSP), in which a set of jobs to be processed is subject to precedence and labor requirement constraints. Each job has a specified processing time and a labor requirements profile, which typically varies as the job is processed. Given the amount of labor available at … Read more
The matrix variables in a primal-dual pair of semidefinite programs are getting increasingly ill-conditioned as they approach a complementary solution. Multiplying the primal matrix variable with a vector from the eigenspace of the non-basic part will therefore result in heavy numerical cancellation. This effect is amplified by the scaling operation in interior point methods. In … Read more