The Geometry of SDP-Exactness in Quadratic Optimization

Diego Cifuentes, Bernd Sturmfels, and Corey Harris

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Submission date: 06. Apr. 2018
Pages: 26
published in: Mathematical programming (2019), pp not yet known
DOI number (of the published article): 10.1007/s10107-019-01399-8
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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.