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Pré-Publication, Document De Travail Année : 2022

Swarm gradient dynamics for global optimization: the density case

Résumé

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 minimizer is 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.
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Dates et versions

hal-03564178 , version 1 (10-02-2022)
hal-03564178 , version 2 (01-04-2022)
hal-03564178 , version 3 (02-12-2022)

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Jérôme Bolte, Laurent Miclo, Stéphane Villeneuve. Swarm gradient dynamics for global optimization: the density case. 2022. ⟨hal-03564178v3⟩
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