The Geometry of SDP-Exactness in Quadratic Optimization
Optimization and Control
2019-01-08 v2 Symbolic Computation
Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1804.01796,
title = {The Geometry of SDP-Exactness in Quadratic Optimization},
author = {Diego Cifuentes and Corey Harris and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1804.01796},
year = {2019}
}
Comments
26 pages, 9 figures