-

 

 

 




Optimization Online





 

DIRECT SEARCH ALGORITHMS OVER RIEMANNIAN MANIFOLDS

David W. Dreisigmeyer (dreisigm***at***lanl.gov)

Abstract: We generalize the Nelder-Mead simplex and LTMADS algorithms and, the frame based methods for function minimization to Riemannian manifolds. Examples are given for functions defined on the special orthogonal Lie group $\mathcal{SO}(n)$ and the Grassmann manifold $\mathcal{G}(n,k)$. Our main examples are applying the generalized LTMADS algorithm to equality constrained optimization problems and, to the Whitney embedding problem for dimensionality reduction of data. A convergence analysis of the frame based method is also given.

Keywords: Direct search methods, Riemannian manifolds, Grassmann manifolds, equality constraints, geodesics

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation:

Download: [PDF]

Entry Submitted: 08/02/2007
Entry Accepted: 08/02/2007
Entry Last Modified: 08/02/2007

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 Programming Society