  Artificial neural networks (ANNs) are used in various applications for
data-driven black-box modeling and subsequent optimization. Herein, we present
an efficient method for deterministic global optimization of ANN embedded
optimization problems. The proposed method is based on relaxations of
algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20
(2009), pp. 573-601] including the convex and concave envelopes of the
nonlinear activation function of ANNs. The optimization problem is solved using
our in-house global deterministic solver MAiNGO. The performance of the
proposed method is shown in four optimization examples: an illustrative
function, a fermentation process, a compressor plant and a chemical process
optimization. The results show that computational solution time is favorable
compared to the global general-purpose optimization solver BARON.
