Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints

Understand

We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman inversion (EKI).

• Unlike other approaches in the literature, the method we propose does not constrain the dynamics to the feasible region of the state space at all times; the particles evolve in the full space, but are attracted towards the feasible set by means of a penalization term added to the objective function and, in the case of CBO, an additional relaxation drift.
• We study the properties of the method through the associated mean-field Fokker--Planck equation and demonstrate its performance in numerical experiments on several test problems.