Below are some links relating to the RTR and to Riemannian Optimization in general. Feel free to email me if you have links that should appear here...
Other Riemannian Optimization Software
SG_Min - Stiefel Grassmann
Provides four iterations for optimization on the Steifel and Grassmann manifolds:
Polak-Ribiere nonlinear CG
Fletcher-Reeves nonlinear CG
Contains applications for nearest degenerate eigenproblems, least square
diagonalization problems, Procrustes problems, and electronic structures problems. Language: MATLAB Author: Ross Lippert
The following lists are intended to be a jumping off point for those looking for
resources on Riemannian optimization. However, they are grossly incomplete.
Please email me when you find neglected works.
Riemannian Optimization Books
Optimization and Dynamical Systems - Helmke and Moore. 1994, Springer-Verlag.
R. L. Adler, J.-P. Dedieu, J. Y. Margulies, M. Martens and M. Shub. Newton's method on Riemannian manifolds and a geometric model for the human spine. IMA J. Numer. Anal. 22(3) (2002) 359-390.
C. G. Baker, P.-A. Absil and K. A. Gallivan. An implicit Riemannian trust-region method for the symmetric generalized eigenproblem. Computational Science - ICCS 2006. Lecture Notes in Computer Science 3991. (2006) 210-217.
H. R. Rutishauser. Simultaneous iteration method for symmetric matrices. Numerische Mathematik 16 (1970) 205-223.
M. Shub. Some remarks on dynamical systems and numerical analysis. In VII ELAM. (1986) 69-92.
S. T. Smith. Geometric optimization methods for adaptive filtering. Ph.D. thesis (1993) Division of Applied Sciences, Harvard University.
S. T. Smith. Optimization techniques on Riemannian manifolds. Hamiltonian and gradient flows, algorithms and control, Fields Inst. Commun. 3. (1994) 113-136.
Y. Yang Optimization on Riemannian manifold. Proceedings of the 38th Conference on Decision and Control (1999)
Y. Yang Globally convergent optimization algorithms on Riemannian manifolds: Uniform framework for unconstrained and constrained optimization. Journal of Optimization Theory and Applications 132(2) (2007) 245-265.