Abstract
This research work originates from a challenging control problem in space engineering that gives rise to hard nonlinear optimization issues. Specifically, we need the piecewise linearization (PL) of a large number of non-convex univariate functions, within a mixed integer linear programming (MILP) framework. For comparative purposes, we recall a well-known classical PL formulation, an alternative approach based on disaggregated convex combination (DCC), and a more recent approach proposed by Vielma and Nemhauser. Our analysis indicates that—in the specific context of our study—the DCC-based approach has computational advantages: this finding is supported by experimental results. We discuss extensions and variations of the basic DCC paradigm. Extensions to a number of possible application areas in robotics and automation are also envisioned.
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Acknowledgements
The authors thank Laureano Escudero for his interest and comments related to the present work.
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Fasano, G., Pintér, J.D. (2019). Efficient Piecewise Linearization for a Class of Non-convex Optimization Problems: Comparative Results and Extensions. In: Pintér, J.D., Terlaky, T. (eds) Modeling and Optimization: Theory and Applications. MOPTA 2017. Springer Proceedings in Mathematics & Statistics, vol 279. Springer, Cham. https://doi.org/10.1007/978-3-030-12119-8_3
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DOI: https://doi.org/10.1007/978-3-030-12119-8_3
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