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A new series of conjectures and open questions in optimization and matrix analysis

Jean-Baptiste Hiriart-Urruty (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.

A nonasymptotic theorem for unnormalized Feynman–Kac particle models

F. Cérou, P. Del Moral, A. Guyader (2011)

Annales de l'I.H.P. Probabilités et statistiques

We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...

A note on order statistics from symmetrically distributed samples

Marek Kałuszka, Andrzej Okolewski (2011)

Applicationes Mathematicae

We present a first moment distribution-free bound on expected values of L-statistics as well as properties of some numerical characteristics of order statistics, in the case when the observations are possibly dependent symmetrically distributed about the common mean. An actuarial interpretation of the presented bound is indicated.

A note on the IPF algorithm when the marginal problem is unsolvable

Claudio Asci, Mauro Piccioni (2003)

Kybernetika

In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2x2x2 contingency table whose pair marginals are all equal to a specified 2x2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occur when the parameter crosses the threshold.

A note on the likelihood and moments of the skew-normal distribution.

Eliseo Martínez, Héctor Varela, Héctor W. Gómez, Heleno Bolfarine (2008)

SORT

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood...

A primal-dual integral method in global optimization

Jens Hichert, Armin Hoffmann, Huan Xoang Phú, Rüdiger Reinhardt (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Using the Fenchel conjugate F c of Phú’s Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.

A reduced basis element method for the steady Stokes problem

Alf Emil Løvgren, Yvon Maday, Einar M. Rønquist (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decompose the computational domain into a series of subdomains that are deformations of a few reference domains (or generic computational parts). Associated with each reference domain are precomputed solutions corresponding to the same...

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