MiS Preprint Repository

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MiS Preprint

The Geometry of SDP-Exactness in Quadratic Optimization

Diego Cifuentes, Bernd Sturmfels and Corey Harris


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.

Apr 6, 2018
Apr 9, 2018

Related publications

2020 Journal Open Access
Diego Cifuentes, Corey Harris and Bernd Sturmfels

The geometry of SDP-exactness in quadratic optimization

In: Mathematical programming, 182 (2020) 1/2, pp. 399-428