Abstract
Determining whether an ellipsoid contains the intersection of many concentric ellipsoids is an NP-hard problem. In this paper, we study various convex relaxations of this problem, namely two semidefinite relaxations and a second-order cone relaxation. We establish some links between these relaxations and perform extensive numerical testings to verify their exactness, their computational load and their stability. As an application of this problem, we study an issue emerging from an aircraft wing design problem: how can we simplify the description of a feasible loads region?
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Adjiashvili, D., Baes, M., Rostalski, P. (2010). Removing Redundant Quadratic Constraints. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_46
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DOI: https://doi.org/10.1007/978-3-642-15582-6_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15581-9
Online ISBN: 978-3-642-15582-6
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