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We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable.
Newton’s method in general analysis
Albert A Bennett · 1916
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Functional analysis and applied mathematics
Leonid Vital’evich Kantorovich · 1948
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Interior-Point Polynomial Algorithms in Convex Programming
Yurii Nesterov and Arkadii Nemirovskii · 1994
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Primal-dual interior-point methods
Stephen J Wright · 1997
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Trust-Region Methods
Andrew R. Conn, Nicholas I. M. Gould, and Philippe L. Toint · 2000
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Accelerating the Cubic Regularization of Newton’s Method on Convex Problems
Yurii Nesterov · 2005
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Cubic regularization of Newton method and its global performance
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Newton-Kantorovich Method and Its Global Convergence
B. T. Polyak · 2006
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Trust Region Newton Method for Logistic Regression
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Katya Scheinberg and Xiaocheng Tang · 2016
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CoCoA: A General Framework for Communication-Efficient Distributed Optimization
Virginia Smith, Simone Forte, Chenxin Ma, Martin Takac, Michael I. Jordan, and Martin Jaggi · 2016
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Matrix Scaling and Balancing via Box Constrained Newton’s Method and Interior Point Methods
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Matilde Gargiani, Celestine Dunner, and Martin Jaggi · 2017
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