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The Geometry of SDP-Exactness in Quadratic Optimization

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arxiv 1804.01796 v2 pith:256BMV6Y submitted 2018-04-05 math.OC cs.SCmath.AG

Diego Cifuentes , Corey Harris , Bernd Sturmfels This is my paper · ORCID
classification math.OCcs.SCmath.AG
keywords problemquadraticobjectiveregionalgebraicboundarybundlecharacterize
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Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance problem, this is a bundle of spectrahedral shadows surrounding the given variety. We characterize the algebraic boundary of this region and we derive a formula for its degree.

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  1. Algebraic Representations for Volumetric Frame Fields

    cs.GR 2019-08 conditional novelty 8.0 of 10

    Octahedral frame space embeds isometrically in R9, giving closed-form geodesics and SDP projection, and a new odeco frame type handles singular curves.

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