Résumé
We introduce and analyse the almost sure convergence of a new stochastic algorithm for the global minimization of Morse functions on compact Riemannian manifolds. This diffusion process is called fraudulent because it requires the knowledge of minimal value of the function to minimize. Its investigation is nevertheless important, since in particular it appears as the limit behavior of non-fraudulent and time-inhomogeneous swarm mean-field algorithms used in global optimization.
Mots-clés
Global optimization; stochastic algorithms; diffusion processes on Riemannian manifolds; almost sure convergence; Morse functions; Bessel processes;
Référence
Laurent Miclo, « On the convergence of global-optimization fraudulent stochastic algorithms », The Annales Henri Lebesgue, vol. 8, 2025, p. 569–587.
Publié dans
The Annales Henri Lebesgue, vol. 8, 2025, p. 569–587