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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 64, 2015 - Issue 4
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Articles

A new, globally convergent Riemannian conjugate gradient method

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Pages 1011-1031 | Received 02 Feb 2013, Accepted 01 Aug 2013, Published online: 20 Sep 2013

References

  • Hestenes MR, Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand. 1952;49: 409–436.
  • Fletcher R, Reeves CM. Function minimization by conjugate gradients. Comput. J. 1964;7:149–154.
  • Nocedal J, Wright SJ. Numerical optimization. 2nd ed. New York: Springer; 2006.
  • Absil P-A, Mahony R, Sepulchre R. Optimization algorithms on matrix manifolds. Princeton (NJ): Princeton University Press; 2008.
  • Edelman A, Arias TA, Smith ST. The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 1998;20:303–353.
  • Smith ST. Optimization techniques on Riemannian manifolds. In: Hamiltonian and gradient flows, algorithms and control. Vol. 3, Fields Institute Communications. Providence (RI): American Mathematical Society; 1994. p. 113–136.
  • Ring W, Wirth B. Optimization methods on Riemannian manifolds and their application to shape space. SIAM J. Optim. 2012;22:596–627.
  • Absil P-A, Malick J. Projection-like retractions on matrix manifolds. SIAM J. Optim. 2012;22:135–158.
  • Al-Baali M. Descent property and global convergence of the Fletcher–Reeves method with inexact line search. I.M.A. J. Numer. Anal. 1985;5:121–124.
  • Helmke U, Moore JB. Optimization and dynamical systems. Communication and Control Engineering Series. Berlin: Springer; 1994.
  • Sato H, Iwai T. A Riemannian optimization approach to the matrix singular value decomposition. SIAM J. Optim. 2013;23:188–212.

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