Riemannian BFGS algorithm with applications

Recent Advances in Optimization and its Applications in Engineering

Volumn , Issue , 2010, Pages 183-192

  Qi, Chunhong ^a   Gallivan, Kyle A ^a   Absil, P A ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84876681866     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-12598-0_16     Document Type: Chapter

References (11)

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2. P.-A. Absil, C. G. Baker, and K. A. Gallivan (2007) Trust-region methods on Riemannian manifolds. Found. Comput. Math., 7(3):303-330
3. P.-A. Absil, R. Mahony, and R. Sepulchre (2008) Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, NJ
4. Roy L. Adler, Jean-Pierre Dedieu, Joseph Y. Margulies, Marco Martens, and Mike Shub (2002) Newton's method on Riemannian manifolds and a geometric model for the human spine. IMA J. Numer. Anal., 22(3):359-390
5. N. Del Buono and C. Elia (2003) Computation of few Lyapunov exponents by geodesic based algorithms. Future Generation Computer systems, 19: 425-430
6. Ian Brace and Jonathan H. Manton (2006) An improved BFGS-on-manifold algorithm for computing weighted low rank approximations. In Proceedings of the 17h International Symposium on Mathematical Theory of Networks and Systems, pages 1735-1738
7. John E. Dennis, Jr. and Robert B. Schnabel (1983) Numerical methods for unconstrained optimization and nonlinear equations. Prentice Hall Series in Computational Mathematics, Prentice Hall Inc., Englewood Cliffs, NJ
8. Alan Edelman, Tomás A. Arias, and Steven T. Smith (1998) The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl., 20(2):303-353
9. D. Gabay (1982) Minimizing a differentiable function over a differential manifold. J. Optim. Theory Appl., 37(2):177-219
10. Jorge Nocedal and Stephen J. Wright (2006) Numerical optimization. Springer Series in Operations Research and Financial Engineering, Springer, New York, second edition
11. Berkant Savas and Lek-Heng Lim (2008) Best multilinear rank approximation of tensors with quasi-Newton methods on Grassmannians. Technical Report LITH-MAT-R-2008-01-SE, Department of Mathematics, Linkôpings University