Octahedral frame space embeds isometrically in R9, giving closed-form geodesics and SDP projection, and a new odeco frame type handles singular curves.
The Geometry of SDP-Exactness in Quadratic Optimization
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abstract
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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2019 1verdicts
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Algebraic Representations for Volumetric Frame Fields
Octahedral frame space embeds isometrically in R9, giving closed-form geodesics and SDP projection, and a new odeco frame type handles singular curves.