The Geometry of SDP-Exactness in Quadratic Optimization

04/05/2018
by   Diego Cifuentes, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset