Bolte, Jérôme, Miclo, Laurent and Villeneuve, Stéphane (2022) Swarm gradient dynamics for global optimization: the mean-field limit case. TSE Working Paper, n. 22-1302, Toulouse, France

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Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge-Kantorovich gradient system formulation with vanishing forces, we formally extend the simulated annealing method to a wide class of global optimization methods. Due to an inbuilt combination of a gradient-like strategy and particles interactions, we call them swarm gradient dynamics. As in the original paper of Holley-Kusuoka-Stroock, the key to the existence of a schedule ensuring convergence to a global minimizeris a functional inequality. One of our central theoretical contributions is the proof of such an inequality for one-dimensional compact manifolds. We conjecture the inequality to be true in a much wider setting. We also describe a general method allowing for global optimization and evidencing the crucial role of functional inequalities à la Łojasiewicz.

Item Type: Monograph (Working Paper)
Language: English
Date: March 2022
Place of Publication: Toulouse, France
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 09 Feb 2022 13:25
Last Modified: 26 Jun 2023 13:10
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