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McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization
Dominik Bongartz, Jaromił Najman, Susanne Sass, Clara Witte, Alexander Mitsos

Thank you for using the beta version of MAiNGO! If you have any issues, concerns, or comments, please communicate them using the "Issues" functionality in GitLab or send an e-mail to


MAiNGO can solve problems of the following form, returning a solution that is delta-feasible and epsilon-optimal (where delta and epsilon are the respective tolerances specified by the user; cf., e.g., M. Locatelli & F. Schoen (2013), Global Optimization: Theory, Algorithms, and Applications) or showing that no delta-feasible point exists:

where the functions f, g and h can be computer codes implementing factorable functions (including multivariate outer functions as introduced by Tsoukalas & Mitsos 2014). For details on what you may or may not do within these functions, see Section Modeling in MAiNGO. Note, however, that the relaxations and most bounding operations are not validated in the sense that round-off error is not accounted for. In this sense, the results cannot be fully guaranteed.

Example Applications

MAiNGO works particularly well for problems which can be formulated in a reduced space manner (Mitsos et al. 2009, Bongartz & Mitsos 2017a).

MAiNGO has been successfully applied to multiple flowsheet-optimization problems (Bongartz & Mitsos 2017a, Bongartz & Mitsos 2017b, Bongartz & Mitsos 2019).

MAiNGO holds specialized relaxations for functions found in the field of chemical engineering (Najman & Mitsos 2016, Najman et al. 2019, Bongartz et al. 2020). All implemented special intrinsic functions can be found in the Library of Functions or doc/implementedFunctions/Implemented_functions.pdf in the MAiNGO git repository.

Example Applications with Machine-Learning models (MeLOn)

MAiNGO automatically includes the "MeLOn - Machine Learning models for Optimization" toolbox as a submodule. MeLOn allows the easy integration of various machine-learning models into optimization problems. Our previous work has shown that the reduced-space formulation and McCormick relaxations used by MAiNGO are favorable for the optimization with machine-learning surrogate models embedded.

MAiNGO and MeLOn have already been used for optimization problems with artificial neural networks embedded (Schweidtmann & Mitsos 2018) and Gaussian processes embedded (Schweidtmann et al. 2020). Machine-learning models have also been combined with mechanistic process models for various applications including membrane science (Rall et al. 2019, Rall et al. 2020a, Rall et al. 2020b), energy process optimization (Schweidtmann et al. 2019, Schweidtmann et al. 2019, Huster et al. 2019a, Huster et al. 2019b), and nonlinear scheduling (Schäfer et al. 2020).

How to Cite MAiNGO

If you use MAiNGO, please cite the MAiNGO report:
Bongartz, D., Najman, J., Sass, S. and Mitsos, A., MAiNGO - McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization. Technical Report, Process Systems Engineering (AVT.SVT), RWTH Aachen University (2018).

Table of Content

This manual is divided in the following sections: