Article Dans Une Revue Evolution Equations and Control Theory Année : 2026

Stochastic Monotone Inclusion with Closed Loop Distributions

Résumé

In this paper, we study in a Hilbertian setting, first and second-order monotone inclusions related to stochastic optimization problems with decision-dependent distributions. The studied dynamics are formulated as monotone inclusions governed by Lipschitz perturbations of maximally monotone operators where the concept of equilibrium plays a central role. We discuss the relationship between the W1-Wasserstein Lipschitz behavior of the distribution and the so-called coarse Ricci curvature. As an application, we consider the monotone inclusions associated with stochastic optimisation problems involving the sum of a smooth function with Lipschitz gradient, a proximable function and a composite term.

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hal-04974921 , version 1 (04-03-2025)

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Hamza Ennaji, Jalal M. Fadili, Hedy Attouch. Stochastic Monotone Inclusion with Closed Loop Distributions. Evolution Equations and Control Theory, 2026, 17, pp.140-172. ⟨10.3934/eect.2025022⟩. ⟨hal-04974921⟩
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