On the convergence of global-optimization fraudulent stochastic algorithms

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 di˙usion process is called fraudulent because it requires the knowledge of minimal value of the function. 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.