An interior point method for nonlinear constrained derivative-free optimization

In this paper we consider constrained optimization problems where both the\nobjective and constraint functions are of the black-box type. Furthermore, we\nassume that the nonlinear inequality constraints are non-relaxable, i.e. their\nvalues and that of the objective function cannot be computed outside of the\nfeasible region. This situation happens frequently in practice especially in\nthe black-box setting where function values are typically computed by means of\ncomplex simulation programs which may fail to execute if the considered point\nis outside of the feasible region. For such problems, we propose a new\nderivative-free optimization method which is based on the use of a merit\nfunction that handles inequality constraints by means of a log-barrier approach\nand equality constraints by means of a quadratic penalty approach. We prove\nconvergence of the proposed method to KKT stationary points of the problem\nunder quite mild assumptions. Furthermore, we also carry out a preliminary\nnumerical experience on standard test problems and comparison with a\nstate-of-the-art solver which shows efficiency of the proposed method.\n