spectral decomposition – Optimization Online

Rank computation in Euclidean Jordan algebras

Published: 2021/07/03, Updated: 2022/04/08

Convex Optimization, Linear, Cone and Semidefinite Programming characteristic polynomial, euclidean jordan algebra, rank, regular element, spectral decomposition

Euclidean Jordan algebras are the abstract foundation for symmetriccone optimization. Every element in a Euclidean Jordan algebra has a complete spectral decomposition analogous to the spectral decomposition of a real symmetric matrix into rank-one projections. The spectral decomposition in a Euclidean Jordan algebra stems from the likewise-analogous characteristic polynomial of its elements, whose degree is … Read more

On efficiently computing the eigenvalues of limited-memory quasi-Newton matrices

Published: 2015/07/10

Jennifer B. Erway

Roummel F. Marcia

Nonlinear Optimization eigenvalues, limited memory quasi-newton methods, qr decomposition, quasi-newton matrices, spectral decomposition

In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that … Read more