In many machine learning applications, one wants to learn the unknown objective and constraint functions of an optimization problem from available data and then apply some technique to attain a local optimizer of the learned model. This work considers Gaussian processes as global surrogate models and utilizes them in conjunction with derivative-free trust-region methods. It is well known that derivative-free trust-region methods converge globally---provided the surrogate model is probabilistically fully linear. We prove that glspl{gp} are indeed probabilistically fully linear, thus resulting in fast (compared to linear or quadratic local surrogate models) and global convergence. We draw upon the optimization of a chemical reactor to demonstrate the efficiency of gls{gp}-based trust-region methods.
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