grassmannian – Optimization Online

Analytic Formulas for Alternating Projection Sequences for the Positive Semidefinite Cone and an Application to Convergence Analysis

Published: 2024/08/17

\(\) We derive analytic formulas for the alternating projection method applied to the cone \(S^n_+\) of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that … Read more

Quasi-Newton methods on Grassmannians and multilinear approximations of tensors

Published: 2009/08/03, Updated: 2010/05/30

Lek-Heng Lim

Berkant Savas

Data-Mining, Nonlinear Optimization approximations, grassmann bfgs, grassmann l-bfgs, grassmann manifold, grassmann quasi-newton, grassmannian, multilinear rank, product of grassmannians, symmetric multilinear rank, symmetric tensor, tensor

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmannians or a product of Grassmannians. Specifically we defined BFGS and L-BFGS updates in local and global coordinates on Grassmannians or a product of these. We proved that, when local coordinates are used, our BFGS updates on Grassmannians share … Read more