A trust-region framework for derivative-free mixed-integer optimization

This paper overviews the development of a framework for the optimization of black-box mixed-integer functions subject to bound constraints. Our methodology is based on the use of tailored surrogate approximations of the unknown objective function, in combination with a trust-region method. To construct suitable model approximations, we assume that the unknown objective is locally quadratic, and we prove that this leads to fully-linear models in restricted discrete neighborhoods. We show that the proposed algorithm converges to a first-order mixed-integer stationary point according to several natural definitions of mixed-integer stationarity, depending on the structure of the objective function. We present numerical results to illustrate the computational performance of different implementations of this methodology in comparison with the state-of-the-art derivative-free solver NOMAD.