The geometry of SDP-exactness in quadratic optimization

Author(s)
Cifuentes, Diego; Harris, Corey; Sturmfels, Bernd
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Abstract
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.
Date issued
2019-05-15
URI
https://hdl.handle.net/1721.1/131668
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Publisher
Springer Berlin Heidelberg
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