Some Recent Developments in Spectrahedral Computation

Thorsten Theobald ()
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Thorsten Theobald: FB 12 – Institut für Mathematik, Goethe-Universität

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 717-739 from Springer

Abstract: 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.

Keywords: Spectrahedron; Spectrahedral computation; Real algebraic geometry; Convex algebraic geometry; Containment; 14Q20; 52A20; 68W30; 90C22 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_30

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DOI: 10.1007/978-3-319-70566-8_30

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