Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
28/2018

The Geometry of SDP-Exactness in Quadratic Optimization

Diego Cifuentes, Bernd Sturmfels and Corey Harris

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.

Received:
Apr 6, 2018
Published:
Apr 9, 2018

Related publications

inJournal
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