C. G. Baker – Optimization Online

An implicit trust-region method on Riemannian manifolds

Published: 2007/06/06

Constrained Nonlinear Optimization optimization on manifolds, symmetric generalized eigenvalue problem, trust-region methods

We propose and analyze an “implicit” trust-region method in the general setting of Riemannian manifolds. The method is implicit in that the trust-region is defined as a superlevel set of the ratio of the actual over predicted decrease in the objective function. Since this method potentially requires the evaluation of the objective function at each … Read more

Convergence analysis of Riemannian trust-region methods

Published: 2006/06/19

Pierre-Antoine Absil

Kyle A. Gallivan

C. G. Baker

Nonlinear Optimization global convergence, local convergence, numerical optimization on manifolds, steihaug-toint, superlinear, symmetric eigenvalue problem, truncated conjugate-gradient, trust-region methods

A general scheme for trust-region methods on Riemannian manifolds is proposed and analyzed. Among the various approaches available to (approximately) solve the trust-region subproblems, particular attention is paid to the truncated conjugate-gradient technique. The method is illustrated on problems from numerical linear algebra. Citation19 June 2006ArticleDownload View PDF