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

Global Deterministic Optimization with Artificial Neural Networks Embedded