Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

Trust-Region Methods

A. R. Conn, N. I. M. Gould, and Ph. L. Toint · 2000

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Introductory lectures on convex optimization

Y. Nesterov · 2004

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Cubic regularization of Newton method and its global performance

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Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results

C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2011

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Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function and derivative-evaluation complexity

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Gradient descent efficiently finds the cubic-regularized nonconvex Newton step

Original

Y. Carmon and J. C. Duchi · 2016

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A trust region algorithm with a worst-case iteration complexity of

F. E. Curtis, D. P. Robinson, and M. Samadi

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Finding approximate local minima faster than gradient descent

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Cubic-regularization counterpart of a variable-norm trust-region method for unconstrained minimization

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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

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The use of quadratic regularization with a cubic descent condition for unconstrained optimization

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A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds

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