Result: On the convergence of global-optimization fraudulent stochastic algorithms

Title:
On the convergence of global-optimization fraudulent stochastic algorithms
Authors:
Miclo, Laurent
Contributors:
Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE-R), Université de Toulouse (UT)-Université de Toulouse (UT)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), AFOSR-22IOE016, ANR-17-EURE-0010,CHESS,Toulouse Graduate School défis en économie et sciences sociales quantitatives(2017)
Source:
https://hal.science/hal-04094950 ; 2023.
Publisher Information:
HAL CCSD
Publication Year:
2023
Collection:
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
Subject Terms:
Global optimization, Stochastic algorithms, Diffusion processes on Riemannian manifolds, Almost sure convergence, Morse functions, Bessel processes, MSC2020: primary: 60J60, secondary: 58J65, 90C26, 65C05, 60F15, 60J35, 35K10, [MATH]Mathematics [math]
Document Type:
Report report
Language:
English
Relation:
hal-04094950; https://hal.science/hal-04094950; https://hal.science/hal-04094950/document; https://hal.science/hal-04094950/file/fraudulent-3.pdf
Availability:
https://hal.science/hal-04094950
https://hal.science/hal-04094950/document
https://hal.science/hal-04094950/file/fraudulent-3.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edsbas.4407C75B
Database:
BASE

Further Information

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. 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.