The geometry of SDP-exactness in quadratic optimization
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10107_2019_Article_1399.pdf
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1.2 MB
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b07402a1196a2b7e544bdd576a49ce2b
Author(s)
Cifuentes, Diego
Harris, Corey
Sturmfels, Bernd
Date Issued
May 15, 2019
Publisher
Springer Berlin Heidelberg
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/s10107-019-01399-8
