tensor – Optimization Online

Symmetric tensor approximation hierarchies for the completely positive cone

Published: 2010/11/03, Updated: 2015/01/18

In this paper we construct two approximation hierarchies for the completely positive cone based on symmetric tensors. We show that one hierarchy corresponds to dual cones of a known polyhedral approximation hierarchy for the copositive cone, and the other hierarchy corresponds to dual cones of a known semidefinite approximation hierarchy for the copositive cone. As … 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