Augmented Lagrangian Constraint Handling for CMA-ES - Case of a Single Linear Constraint

We consider the problem of minimizing a function f subject to a single inequality constraint \(g(\mathbf x ) \le 0\), in a black-box scenario. We present a covariance matrix adaptation evolution strategy using an adaptive augmented Lagrangian method to handle the constraint. We show that our algorithm is an instance of a general framework that allows to build an adaptive constraint handling algorithm from a general randomized adaptive algorithm for unconstrained optimization. We assess the performance of our algorithm on a set of linearly constrained functions, including convex quadratic and ill-conditioned functions, and observe linear convergence to the optimum.