Swarm gradient dynamics for global optimization: the mean-field limit case

Stéphane Villeneuve, Jérôme Bolte and Laurent Miclo

No 22-1302, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: 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.

Date: 2022-03
New Economics Papers: this item is included in nep-ore
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Working Paper: Swarm gradient dynamics for global optimization: the mean-field limit case (2024)
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