We consider the integer program P -> max {c’x | Ax=y; x\in N^n }. Using the generating function of an associated counting problem, and a generalized residue formula of Brion and Vergne, we explicitly relate P with its continuous linear programming (LP) analogue and provide a characterization of its optimal value. In particular, dual variables … Read more
Let f be a lower semi-continuous convex function in a Euclidean space, finite or infinite dimensional. The gradient differential inclusion is a generalized differential equation which requires that -x'(t) be in the subgradient of f at x. It is the continuous versions of the gradient descent method for minimizing f in case f is differentiable, … Read more
This paper is concerned with the study of envelope theorems for finite choice sets. More specifically, we consider the problem of differentiability of the value function arising out of the maximization of a parametrized objective function, when the set of alternatives is non-empty and finite. The parameter is confined to the closed interval [0,1] and … Read more
CitationResearch report, PCS Inc., Halifax, NS, Canada; November 2003. Submitted for publication.ArticleDownload View PDF
Density estimation is a classical and important problem in statistics. The aim of this paper is to develop a new computational approach to density estimation based on semidefinite programming (SDP), a new technology developed in optimization in the last decade. We express a density as the product of a nonnegative polynomial and a base density … Read more
The safe dissemination of statistical tabular data is one of the main concerns of National Statistical Institutes (NSIs). Although each cell of the tables is made up of the aggregated information of several individuals, the statistical confidentiality can be violated. NSIs must guarantee that no individual information can be derived from the released tables. One … Read more
This article presents a non-parametric statistical test that is very interesting for those who want to compare different heuristic algorithms that do not necessarily end with feasible (or satisfying) solutions. This test has been specially designed for working with very small sample sizes, meaning that a substantial computational effort can be saved when conducting numerical … Read more
Primal-Dual Interior-Point Methods (IPMs) have shown their power in solving large classes of optimization problems. However, there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results with respect to the update strategies of the duality gap parameter in the algorithm. The so-called small-update IPMs enjoy the best … Read more
We present results on global and polynomial-time convergence of infeasible-interior-point methods for self-scaled conic programming, which includes linear and semidefinite programming. First, we establish global convergence for an algorithm using a wide neighborhood. Next, we prove polynomial complexity for the algorithm with a slightly narrower neighborhood. Both neighborhoods are related to the wide (minus infinity) … Read more
This paper presents a fuzzy control approach for improving convergence time in stochastic global minimization algorithms .We show concrete results when the method is applied to an efficient algorithm based on ideas related to Simulated Annealing. ArticleDownload View PDF