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Second-order methods, which utilize gradients as well as Hessians to optimize a given function, are of major importance in mathematical optimization.
Functional analysis and applied mathematics
Leonid Vital’evich Kantorovich · 1948
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Problem Complexity and Method Efficiency in Optimization
Arkadi Nemirovsky and David Yudin · 1983
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A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2})
Yurii Nesterov · 1983
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Interior-point polynomial algorithms in convex programming
Yurii Nesterov and Arkadii Nemirovskii · 1994
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Trust region methods
Andrew R Conn, Nicholas IM Gould, and Philippe L Toint · 2000
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Introductory lectures on convex optimization: A basic course , volume 87
Yurii Nesterov · 2004
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Efficient methods in convex programming – lecture notes, 2005
Arkadi Nemirovski · 2005
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Cubic regularization of newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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Accelerating the cubic regularization of newton’s method on convex problems
Yurii Nesterov · 2008
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Estimate sequence methods: extensions and approximations
Michel Baes · 2009
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Self-concordant analysis for logistic regression
Francis Bach · 2010
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On the complexity of steepest descent, newton’s and regularized newton’s methods for nonconvex unconstrained optimization problems
Coralia Cartis, Nicholas IM Gould, and Philippe L Toint · 2010
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Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
Coralia Cartis, Nicholas IM Gould, and Philippe L Toint · 2012
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An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods
Renato DC Monteiro and Benar Fux Svaiter · 2013
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On uniformly convex functionals
AA Vladimirov, Yu E Nesterov, and Yu N Chekanov · 2013
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Successive rank-one approximations for nearly orthogonally decomposable symmetric tensors
Cun Mu, Daniel Hsu, and Donald Goldfarb · 2015
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Optimal black-box reductions between optimization objectives
Zeyuan Allen-Zhu and Elad Hazan · 2016
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