A Stochastic Algorithm for Global Optimization with application to M-estimators computation

Nabil Rachdi (1, 2) , Jean-Claude Fort (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 EADS Innovation Works [Toulouse]
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Most of statistical procedures consist on estimating parameters by minimizing (or maximizing) some criterion. A minimizing parameter is also called in the literature M-estimator, [2]. Depending on the statistical problem and the available information, the criterion may be more or less complicated: non convex, no gradient, non smooth etc... Thus, it can be difficult in practice to compute an M-estimator. We propose a new algorithm to compute the parameters, mixing stochastic algorithms and smoothness technics. We will call it S2Dyn for Stochastic & Smooth Dynamic algorithm.

Mots clés: M-estimators; Stochastic algorithms; Optimization

Domaines: Calcul [stat.CO]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Nabil Rachdi, Jean-Claude Fort. A Stochastic Algorithm for Global Optimization with application to M-estimators computation. 2011. ⟨hal-00564602v2⟩