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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory pp 717–739Cite as

Some Recent Developments in Spectrahedral Computation

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Abstract

Spectrahedra are the feasible sets of semidefinite programming and provide a central link between real algebraic geometry and convex optimization. In this expository paper, we review some recent developments on effective methods for handling spectrahedra. In particular, we consider the algorithmic problems of deciding emptiness of spectrahedra, boundedness of spectrahedra as well as the question of containment of a spectrahedron in another one. These problems can profitably be approached by combinations of methods from real algebra and optimization.

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Acknowledgements

The author was partially supported through DFG grant 1333/3-1 within the Priority Program 1489 “Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory.”

He would also like to thank an anonymous referee for careful reading and helpful suggestions.

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Authors and Affiliations

  1. Goethe-Universität, FB 12 – Institut für Mathematik, Postfach 11 19 32, 60054, Frankfurt am Main, Germany

    Thorsten Theobald

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  1. Thorsten Theobald
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Correspondence to Thorsten Theobald .

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Editors and Affiliations

  1. IWR, Heidelberg University, Heidelberg, Germany

    Gebhard Böckle

  2. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Wolfram Decker

  3. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Gunter Malle

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Theobald, T. (2017). Some Recent Developments in Spectrahedral Computation. In: Böckle, G., Decker, W., Malle, G. (eds) Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-70566-8_30

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