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This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian structure is sought on a quotient manifold.
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Absil PA, Trumpf J, Mahony R, Andrews B (2009) All roads lead to Newton: Feasible second-order methods for equality-constrained optimization. Tech. rep., UCL-INMA-2009.024
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Theis FJ, Cason TP, Absil PA (2009) Soft dimension reduction for ICA by joint diagonalization on the Stiefel manifold. In: Independent Component Analysis and Signal Separation, Springer Berlin Heidelberg, Berlin, Germany, pp 354–361
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Benner P, Saak J (2013) Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey. GAMM-Mitteilungen 36(1):32–52
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Vandereycken B (2013) Low-rank matrix completion by Riemannian optimization. SIAM Journal on Optimization 23(2):1214–1236
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Absil PA, Amodei L, Meyer G (2014) Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries. Computational Statistics 29(3–4):569–590
2014
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Boumal N, Mishra B, Absil PA, Sepulchre R (2014) Manopt: a Matlab toolbox for optimization on manifolds. Journal of Machine Learning Research 15(Apr):1455–1459
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Mishra B, Sepulchre R (2014) R3MC: A Riemannian three-factor algorithm for low-rank matrix completion. In: Proceedings of the 53rd IEEE Conference on Decision and Control (CDC), pp 1137–1142
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Mishra B, Vandereycken B (2014) A Riemannian approach to low-rank algebraic Riccati equations. In: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS), pp 965–968
2014
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Mishra B, Meyer G, Bonnabel S, Sepulchre R (2014) Fixed-rank matrix factorizations and Riemannian low-rank optimization. Computational Statistics 29(3–4):591–621
2014
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