Swarm dynamics for global optimization on finite sets

Nhat-Thang Le and Laurent Miclo

Stochastic Processes and their Applications, 2026, vol. 191, issue C

Abstract: Consider the global optimisation of a function U defined on a finite set V endowed with an irreducible and reversible Markov generator. By integration, we extend U to the set P(V) of probability distributions on V and we penalize it with a time-dependent generalized entropy functional. Endowing P(V) with a Maas’ Wasserstein-type Riemannian structure enables us to consider an associated time-inhomogeneous gradient descent algorithm. There are several ways to interpret this P(V)-valued dynamical system as the time-marginal laws of a time-inhomogeneous non-linear Markov process taking values in V, each of them allowing for interacting particle approximations. This procedure extends to the discrete framework the continuous state space swarm algorithm approach of Bolte et al. (2023), but here we go further by considering more general generalized entropy functionals for which functional inequalities can be proven. Thus in the full generality of the above finite framework, we give conditions on the underlying time dependence ensuring the convergence of the algorithm toward laws supported by the set of global minima of U. Numerical simulations illustrate that one has to be careful about the choice of the time-inhomogeneous non-linear Markov process interpretation.

Keywords: Finite global optimization; Swarm algorithms; Non-linear finite Markov processes; Interacting particle systems; Maas’ Wasserstein-like metrics; Generalized entropies; Gradient flows; Functional inequalities (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414925002248
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002248

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2025.104780

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().