Trust-Region Methods on Riemannian Manifolds

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. 65K05 Mathematical programming: Algorithms; 65J05 Numerical analybstract spaces; 90C26 Nonconvex programming; 90C48 Programming act spaces; 58C05 Real-valued functions on manifolds Key words. Numerical optimization on manifolds, trust-region, truncated conjugate-gradient, Steihaug-Toint, global convergence, local convergence, superlinear convergence, symmetric eigenvalue problem.

• Type: Journal
• Year: 2007
• Where: FOCM
• Authors: Pierre-Antoine Absil, C. G. Baker, Kyle A. Gallivan
• Keywords: FOCM 2007, Manifolds, Manifolds Key Words, Riemannian Manifolds