From Nesterov's Estimate Sequence to Riemannian Acceleration
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[1] A. M. Lyapunov. The general problem of the stability of motion , 1992 .
[2] Sébastien Bubeck,et al. Introduction to Online Optimization , 2011 .
[3] Bikash Joshi,et al. An Explicit Convergence Rate for Nesterov's Method from SDP , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).
[4] H. E. Rauch,et al. A CONTRIBUTION TO DIFFERENTIAL GEOMETRY IN THE LARGE , 1951 .
[5] Kwangjun Ahn. From Proximal Point Method to Nesterov's Acceleration , 2020, ArXiv.
[6] Michael I. Jordan,et al. On Symplectic Optimization , 2018, 1802.03653.
[7] Andre Wibisono,et al. A variational perspective on accelerated methods in optimization , 2016, Proceedings of the National Academy of Sciences.
[8] Suvrit Sra,et al. An Estimate Sequence for Geodesically Convex Optimization , 2018, COLT.
[9] John Darzentas,et al. Problem Complexity and Method Efficiency in Optimization , 1983 .
[10] Jelena Diakonikolas,et al. The Approximate Duality Gap Technique: A Unified Theory of First-Order Methods , 2017, SIAM J. Optim..
[11] Zeyuan Allen Zhu,et al. Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent , 2014, ITCS.
[12] Jefferson G. Melo,et al. Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds , 2016, Journal of Optimization Theory and Applications.
[13] Francis Bach,et al. Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions , 2019, COLT.
[14] Bin Hu,et al. Dissipativity Theory for Nesterov's Accelerated Method , 2017, ICML.
[15] Antonio Orvieto,et al. A Continuous-time Perspective for Modeling Acceleration in Riemannian Optimization , 2020, AISTATS.
[16] Peter Bürgisser,et al. Towards a Theory of Non-Commutative Optimization: Geodesic 1st and 2nd Order Methods for Moment Maps and Polytopes , 2019, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS).
[17] Suvrit Sra,et al. First-order Methods for Geodesically Convex Optimization , 2016, COLT.
[18] Navin Goyal,et al. Sampling and Optimization on Convex Sets in Riemannian Manifolds of Non-Negative Curvature , 2019, COLT.
[19] Hiroyuki Kasai,et al. Riemannian stochastic variance reduced gradient on Grassmann manifold , 2016, ArXiv.
[20] Marc Teboulle,et al. Performance of first-order methods for smooth convex minimization: a novel approach , 2012, Math. Program..
[21] Pan Zhou,et al. Faster First-Order Methods for Stochastic Non-Convex Optimization on Riemannian Manifolds , 2021, IEEE Transactions on Pattern Analysis and Machine Intelligence.
[22] Hong Cheng,et al. Accelerated First-order Methods for Geodesically Convex Optimization on Riemannian Manifolds , 2017, NIPS.
[23] M. Bacák. Convex Analysis and Optimization in Hadamard Spaces , 2014 .
[24] Stephen P. Boyd,et al. A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights , 2014, J. Mach. Learn. Res..
[25] Bryan Van Scoy,et al. Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees , 2018, ICML.
[26] M. Gromov. Manifolds of negative curvature , 1978 .
[27] Asuman E. Ozdaglar,et al. Robust Accelerated Gradient Methods for Smooth Strongly Convex Functions , 2018, SIAM J. Optim..
[28] Suvrit Sra,et al. Nonconvex stochastic optimization on manifolds via Riemannian Frank-Wolfe methods , 2019, ArXiv.
[29] Sebastian Ehrlichmann,et al. Metric Spaces Of Non Positive Curvature , 2016 .
[30] Robert E. Mahony,et al. Optimization Algorithms on Matrix Manifolds , 2007 .
[31] Jonathan W. Siegel. Accelerated Optimization with Orthogonality Constraints , 2019, 1903.05204.
[32] Michael I. Jordan,et al. A Lyapunov Analysis of Momentum Methods in Optimization , 2016, ArXiv.
[33] J. Jost. Riemannian geometry and geometric analysis , 1995 .
[34] Emmanuel J. Candès,et al. Adaptive Restart for Accelerated Gradient Schemes , 2012, Foundations of Computational Mathematics.
[35] Suvrit Sra,et al. Nonconvex stochastic optimization on manifolds via Riemannian Frank-Wolfe methods , 2019, ArXiv.
[36] C. Udriste,et al. Convex Functions and Optimization Methods on Riemannian Manifolds , 1994 .
[37] Ramsay Dyer,et al. Riemannian simplices and triangulations , 2015 .
[38] Hongyi Zhang,et al. R-SPIDER: A Fast Riemannian Stochastic Optimization Algorithm with Curvature Independent Rate , 2018, ArXiv.
[39] Bin Shi. Acceleration via Symplectic Discretization of High-Resolution Differential Equations , 2019 .
[40] Suvrit Sra,et al. Fast stochastic optimization on Riemannian manifolds , 2016, ArXiv.
[41] Donghwan Kim,et al. Optimized first-order methods for smooth convex minimization , 2014, Math. Program..
[42] Anupam Gupta,et al. Potential-Function Proofs for Gradient Methods , 2019, Theory Comput..
[43] A. V. Gasnikov,et al. Universal Method for Stochastic Composite Optimization Problems , 2018 .
[44] Y. Nesterov. A method for unconstrained convex minimization problem with the rate of convergence o(1/k^2) , 1983 .
[45] R. McCann,et al. A Riemannian interpolation inequality à la Borell, Brascamp and Lieb , 2001 .
[46] Benjamin Recht,et al. Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints , 2014, SIAM J. Optim..
[47] G. Perelman. Spaces with Curvature Bounded Below , 1995 .
[48] Bin Hu,et al. A Robust Accelerated Optimization Algorithm for Strongly Convex Functions , 2017, 2018 Annual American Control Conference (ACC).
[49] Nicolas Boumal,et al. Adaptive regularization with cubics on manifolds , 2018, Mathematical Programming.