5 citations · 10 across the 16 of their papers we have counts for
16 papers
Convergence of time-discrete finite particle consensus based optimization in Hilbert spaces
Michael Herty, Hui Huang, Hicham Kouhkouh
We study a time-discrete, finite-particle Consensus-Based Optimization (CBO) algorithm in a separable Hilbert space. Our analysis provides convergence guarantees directly for the c…
A derivative-free particle method for optimization in Hilbert spaces
Hui Huang, Hicham Kouhkouh
We introduce a stochastic interacting particle system in separable Hilbert spaces together with its associated mean-field formulation. The model is shown to retain the characterist…
Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties
Yuyang Huang, Dante Kalise, Hicham Kouhkouh
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem c…
Non-Convex Global Optimization as an Optimal Stabilization Problem: Convergence Rates
Yuyang Huang, Dante Kalise, Hicham Kouhkouh
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-conve…
Faithful global convergence for the rescaled Consensus-Based Optimization
Hui Huang, Hicham Kouhkouh, Lukang Sun
We analyze the Consensus-Based Optimization (CBO) algorithm with a consensus point rescaled by a small fixed parameter . Under minimal assumptions on the objective func…
Self-interacting CBO: Existence, uniqueness, and long-time convergence
Hui Huang, Hicham Kouhkouh
A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invarian…
Uniform-in-time mean-field limit estimate for the Consensus-Based Optimization
Hui Huang, Hicham Kouhkouh
We establish a uniform-in-time estimate for the mean-field convergence of the Consensus-Based Optimization (CBO) algorithm by rescaling the consensus point in the dynamics with a s…
A multiscale Consensus-Based algorithm for multi-level optimization
Michael Herty, Yuyang Huang, Dante Kalise +1
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the pr…
A viscous ergodic problem with unbounded and measurable ingredients. Part 2: Mean-Field Games
Hicham Kouhkouh
We address the problem of existence and (non-)uniqueness of solutions to ergodic mean-field games in the whole space with unbounded and me…
A viscous ergodic problem with unbounded and measurable ingredients. Part 1: HJB Equation
Hicham Kouhkouh
We address the problem of existence and uniqueness of solutions to ergodic Hamilton-Jacobi-Bellman (HJB) equations of the form in t…
Relaxation and asymptotic expansion of controlled stiff differential equations
Michael Herty, Hicham Kouhkouh
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly per…
Long-time behaviour of deterministic Mean Field Games with non-monotone interactions
Martino Bardi, Hicham Kouhkouh
We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in…
Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
Martino Bardi, Hicham Kouhkouh
We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the Entropic Gradient Descent in t…
Singular perturbations in stochastic optimal control with unbounded data
Martino Bardi, Hicham Kouhkouh
We study singular perturbations of a class of two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neur…
An Eikonal equation with vanishing Lagrangian arising in Global Optimization
Martino Bardi, Hicham Kouhkouh
We show a connection between global unconstrained optimization of a continuous function and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solu…
The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems
Carlos Esteve, Hicham Kouhkouh, Dario Pighin +1
We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal…