RIEMANNIAN MANIFOLD TRUST-REGION METHODS WITH APPLICATIONS TO EIGENPROBLEMS
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[1] I. Holopainen. Riemannian Geometry , 1927, Nature.
[2] J. Nash. The imbedding problem for Riemannian manifolds , 1956 .
[3] H. Rutishauser. Simultaneous iteration method for symmetric matrices , 1970 .
[4] D. Luenberger. The Gradient Projection Method Along Geodesics , 1972 .
[5] W. Boothby. An introduction to differentiable manifolds and Riemannian geometry , 1975 .
[6] M. Powell. CONVERGENCE PROPERTIES OF A CLASS OF MINIMIZATION ALGORITHMS , 1975 .
[7] J. Dennis,et al. Two new unconstrained optimization algorithms which use function and gradient values , 1979 .
[8] Richard H. Byrd,et al. A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties. , 1985 .
[9] D. Sorensen. Newton's method with a model trust region modification , 1982 .
[10] T. Steihaug. The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .
[11] Jorge J. Moré,et al. Computing a Trust Region Step , 1983 .
[12] B. O'neill. Semi-Riemannian Geometry With Applications to Relativity , 1983 .
[13] Ahmed H. Sameh,et al. Trace Minimization Algorithm for the Generalized Eigenvalue Problem , 1982, PPSC.
[14] Richard H. Byrd,et al. Approximate solution of the trust region problem by minimization over two-dimensional subspaces , 1988, Math. Program..
[15] C. Udriste,et al. Convex Functions and Optimization Methods on Riemannian Manifolds , 1994 .
[16] H. A. V. D. Vorsty. University Utrecht a Generalized Jacobi-davidson Iteration Method for Linear Eigenvalue Problems a Generalized Jacobi-davidson Iteration Method for Linear Eigenvalue Problems , 1994 .
[17] Dimitri P. Bertsekas,et al. Nonlinear Programming , 1997 .
[18] H. V. D. Vorst,et al. Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems , 1995 .
[19] U. Helmke,et al. Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.
[20] Gerard L. G. Sleijpen,et al. A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM J. Matrix Anal. Appl..
[21] R. Mahony. The constrained newton method on a Lie group and the symmetric eigenvalue problem , 1996 .
[22] Alan Edelman,et al. The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..
[23] Stephen J. Wright,et al. Numerical Optimization , 2018, Fundamental Statistical Inference.
[24] A. Iserles,et al. Methods for the approximation of the matrix exponential in a Lie‐algebraic setting , 1999, math/9904122.
[25] Nicholas I. M. Gould,et al. Solving the Trust-Region Subproblem using the Lanczos Method , 1999, SIAM J. Optim..
[26] B. Owren,et al. The Newton Iteration on Lie Groups , 2000 .
[27] A. Sameh,et al. The trace minimization method for the symmetric generalized eigenvalue problem , 2000 .
[28] Nicholas I. M. Gould,et al. Trust Region Methods , 2000, MOS-SIAM Series on Optimization.
[29] William W. Hager,et al. Minimizing a Quadratic Over a Sphere , 2001, SIAM J. Optim..
[30] Andrew V. Knyazev,et al. Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method , 2001, SIAM J. Sci. Comput..
[31] Lars Eldén,et al. Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold , 2002, SIAM J. Matrix Anal. Appl..
[32] Yvan Notay,et al. Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem , 2002, Numer. Linear Algebra Appl..
[33] R. Adler,et al. Newton's method on Riemannian manifolds and a geometric model for the human spine , 2002 .
[34] Jonathan H. Manton,et al. Optimization algorithms exploiting unitary constraints , 2002, IEEE Trans. Signal Process..
[35] Robert E. Mahony,et al. A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces , 2002, SIAM Rev..
[36] Mark Frederick Hoemmen,et al. An Overview of Trilinos , 2003 .
[37] K. Huper,et al. Newton-like methods for numerical optimization on manifolds , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..
[38] P. Absil,et al. Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation , 2004 .
[39] P. Absil,et al. Trust-region methods on Riemannian manifolds with applications in numerical linear algebra , 2004 .
[40] Nicholas I. M. Gould,et al. A Filter-Trust-Region Method for Unconstrained Optimization , 2005, SIAM J. Optim..
[41] Pierre-Antoine Absil,et al. Adaptive Model Trust Region Methods for Generalized Eigenvalue Problems , 2005, International Conference on Computational Science.
[42] Jean-Pierre Dedieu,et al. Symplectic methods for the approximation of the exponential map and the Newton iteration on Riemannian submanifolds , 2005, J. Complex..
[43] Jérome M. B. Walmag,et al. A Note on Trust-Region Radius Update , 2005, SIAM J. Optim..
[44] Richard B. Lehoucq,et al. Basis selection in LOBPCG , 2006, J. Comput. Phys..
[45] P. Absil,et al. A truncated-CG style method for symmetric generalized eigenvalue problems , 2006 .
[46] Robert E. Mahony,et al. Optimization Algorithms on Matrix Manifolds , 2007 .
[47] Yaguang Yang. Globally Convergent Optimization Algorithms on Riemannian Manifolds: Uniform Framework for Unconstrained and Constrained Optimization , 2007 .
[48] Pierre-Antoine Absil,et al. Trust-Region Methods on Riemannian Manifolds , 2007, Found. Comput. Math..
[49] Pierre-Antoine Absil,et al. Accelerated Line-search and Trust-region Methods , 2009, SIAM J. Numer. Anal..