Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints
José A. Carrillo, Claudia Totzeck, Urbain Vaes
Abstract
We introduce a practical method for incorporating equality and inequality\nconstraints in global optimization methods based on stochastic interacting\nparticle systems, specifically consensus-based optimization (CBO) and ensemble\nKalman inversion (EKI). Unlike other approaches in the literature, the method\nwe propose does not constrain the dynamics to the feasible region of the state\nspace at all times; the particles evolve in the full space, but are attracted\ntowards the feasible set by means of a penalization term added to the objective\nfunction and, in the case of CBO, an additional relaxation drift. We study the\nproperties of the method through the associated mean-field Fokker--Planck\nequation and demonstrate its performance in numerical experiments on several\ntest problems.\n