A New Computational Approach to Density Estimation with Semidefinite Programming

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

An Adaptive Self-Regular Proximity Based Large-Update IPM for LO

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

A Statistical Test for Comparing Success Rates

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

Quadratic interior-point methods in statistical disclosure control

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

Convergence of infeasible-interior-point methods for self-scaled conic programming

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

Fuzzy Control of Stochastic Global Optimization Algorithms and Very Fast Simulated Reannealing

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. Article Download View Fuzzy Control of Stochastic Global Optimization Algorithms and Very Fast Simulated Reannealing

An interior-point L1-penalty method for nonlinear optimization

A mixed interior/exterior-point method for nonlinear programming is described, that handles constraints by an L1-penalty function. A suitable decomposition of the penalty terms and embedding of the problem into a higher-dimensional setting leads to an equivalent, surprisingly regular, reformulation as a smooth penalty problem only involving inequality constraints. The resulting problem may then be tackled … Read more

A Parallel Primal-Dual Interior-Point Method for Semidefinite Programs Using Positive Definite Matrix Completion

A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of … Read more

On the optimal parameter of a self-concordant barrier over a symmetric cone

The properties of the barrier F(x)=-log(det(x)), defined over the cone of squares of an Euclidean Jordan algebra, are analyzed using pure algebraic techniques. Furthermore, relating the Carathéodory number of a symmetric cone with the rank of an underlying Euclidean Jordan algebra, conclusions about the optimal parameter of F are suitably obtained. Namely, it is proved … Read more