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We consider the minimization of a cost function $f$ on a manifold $M$ using Riemannian gradient descent and Riemannian trust regions (RTR).
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Newton’s method on Riemannian manifolds and a geometric model for the human spine
R. Adler, J. Dedieu, J. Margulies, M. Martens, and M. Shub · 2002
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A. Ruszczyński · 2006
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Trust-region methods on Riemannian manifolds
P.-A. Absil, C. G. Baker, and K. A. Gallivan · 2007
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Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2008
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Riemannian SVRG: Fast stochastic optimization on Riemannian manifolds
H. Zhang, S. Reddi, and S. Sra · 2008
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All roads lead to Newton: Feasible second-order methods for equality-constrained optimization
P.-A. Absil, J. Trumpf, R. Mahony, and B. Andrews · 2009
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On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems
C. Cartis, N. I. M. Gould, and P. L. Toint · 2010
Low-rank retractions: a survey and new results
P.-A. Absil and I. Oseledets · 2015
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A Broyden class of quasi-Newton methods for Riemannian optimization
W. Huang, K. Gallivan, and P.-A. Absil · 2015
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On the low-rank approach for semidefinite programs arising in synchronization and community detection
A. Bandeira, N. Boumal, and V. Voroninski · 2016
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Global optimality of local search for low rank matrix recovery
S. Bhojanapalli, B. Neyshabur, and N. Srebro · 2016
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Nonconvex phase synchronization
N. Boumal · 2016
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The non-convex Burer–Monteiro approach works on smooth semidefinite programs
N. Boumal, V. Voroninski, and A. Bandeira · 2016
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Complexity bounds for second-order optimality in unconstrained optimization
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Two proposals for robust PCA using semidefinite programming
M. McCoy and J. Tropp · 2011
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Numerical optimization methods on Riemannian manifolds
C. Qi · 2011
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Projection-like retractions on matrix manifolds
P.-A. Absil and J. Malick · 2012
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Matrix computations , volume 3 of Johns Hopkins Studies in the Mathematical Sciences
G. Golub and C. Van Loan · 2012
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Optimization methods on Riemannian manifolds and their application to shape space
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Matrix completion has no spurious local minimum
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Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
E. Birgin, J. Gardenghi, J. Martínez, S. Santos, and P. Toint · 2017
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Second-order optimality and beyond: Characterization and evaluation complexity in convexly constrained nonlinear optimization
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Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality
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