Abstract
The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, we address applications, where nonconvexity in the model poses principal difficulties. This paper summarizes the dissertation of the author for the occasion of the GOR dissertation award 2018. We focus on the work on non-convex quad ratic programs and show how problem specific structure can be used to obtain tight relaxations and speed up Branch-and-bound methods. Both a classic general QP and the Pooling Problem as an important practical application serve as showcases.
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Acknowledgements
The author thanks Pierre Bonami, Claudia D’Ambrosio, Jeff Linderoth, Andrea Lodi, Jim Luedtke, and Andrea Tramontani for the joint work.
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Schweiger, J. (2019). Exploiting Structure in Non-convex Quadratic Optimization. In: Fortz, B., Labbé, M. (eds) Operations Research Proceedings 2018. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-18500-8_7
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DOI: https://doi.org/10.1007/978-3-030-18500-8_7
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