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

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  • Villeneuve, Stéphane
  • Bolte, Jérôme
  • Miclo, Laurent

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.

Suggested Citation

  • Villeneuve, Stéphane & Bolte, Jérôme & Miclo, Laurent, 2022. "Swarm gradient dynamics for global optimization: the mean-field limit case," TSE Working Papers 22-1302, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:126578
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    References listed on IDEAS

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    1. Arnak S. Dalalyan, 2017. "Theoretical guarantees for approximate sampling from smooth and log-concave densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 651-676, June.
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    Cited by:

    1. Miclo, Laurent, 2023. "On the convergence of global-optimization fraudulent stochastic algorithms," TSE Working Papers 23-1437, Toulouse School of Economics (TSE).

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