-

 

 

 




Optimization Online





 

The Riemannian Barzilai-Borwein method with nonmonotone line search and the matrix geometric mean computation

Bruno Iannazzo (bruno.iannazzo***at***dmi.unipg.it)
Margherita Porcelli (margherita.porcelli***at***unifi.it)

Abstract: The Barzilai-Borwein method, an effective gradient descent method with clever choice of the step-length, is adapted from nonlinear optimization to Riemannian manifold optimization. More generally, global convergence of a nonmonotone line-search strategy for Riemannian optimization algorithms is proved under some standard assumptions. By a set of numerical tests, the Riemannian Barzilai-Borwein method with nonmonotone line-search is shown to be competitive in several Riemannian optimization problems. When used to compute the matrix geometric mean, known as the Karcher mean of positive definite matrices, it notably outperforms existing first-order optimization methods.

Keywords: Riemannian optimization; manifold optimization; Barzilai-Borwein algorithm; nonmonotone line-search; Karcher mean; matrix geometric mean; positive definite matrix.

Category 1: Nonlinear Optimization (Other )

Citation: IMA Journal of Numerical Analysis, (2017) drx015. doi: 10.1093/imanum/drx015

Download: [PDF]

Entry Submitted: 12/23/2015
Entry Accepted: 12/23/2015
Entry Last Modified: 05/10/2017

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society