11 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: 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 fun…
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…
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…