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Optimization Methods and Software Volume 27, 2012 - Issue 2: Special issue dedicated to Andreas Griewank on the occasion of his 60th birthday
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Original Articles

Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization

Coralia Cartis School of Mathematics, University of Edinburgh, The King's Buildings, Edinburgh, EH9 3JZ, UKCorrespondence[email protected]
,
Nicholas I.M. Gould Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, UK
&
Philippe L. Toint Department of Mathematics, FUNDP – University of Namur, 61, rue de Bruxelles, B-5000, Namur, Belgium
Pages 197-219 | Received 06 Nov 2010, Accepted 27 Jun 2011, Published online: 28 Oct 2011

Citations (15)

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Read on this site (2)

R. Garmanjani. (2022) A note on the worst-case complexity of nonlinear stepsize control methods for convex smooth unconstrained optimization. Optimization 71:6, pages 1709-1719.
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G.N. Grapiglia, J. Yuan & Y. Yuan. (2016) On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization. Optimization Methods and Software 31:3, pages 591-604.
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Articles from other publishers (13)

Jianyu Xiao, Haibin Zhang & Huan Gao. (2023) An Accelerated Regularized Chebyshev–Halley Method for Unconstrained Optimization. Asia-Pacific Journal of Operational Research.
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Nikita Doikov & Yurii Nesterov. (2021) Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method. Journal of Optimization Theory and Applications 189:1, pages 317-339.
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Yurii Nesterov. (2019) Implementable tensor methods in unconstrained convex optimization. Mathematical Programming 186:1-2, pages 157-183.
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Shambhavi Singh & Yves Lucet. (2021) Linear-Time Convexity Test for Low-Order Piecewise Polynomials. SIAM Journal on Optimization 31:1, pages 972-990.
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Peng Xu, Fred Roosta & Michael W. Mahoney. (2019) Newton-type methods for non-convex optimization under inexact Hessian information. Mathematical Programming 184:1-2, pages 35-70.
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Bo Jiang, Tianyi Lin & Shuzhong Zhang. (2020) A Unified Adaptive Tensor Approximation Scheme to Accelerate Composite Convex Optimization. SIAM Journal on Optimization 30:4, pages 2897-2926.
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Yossi Arjevani, Ohad Shamir & Ron Shiff. (2018) Oracle complexity of second-order methods for smooth convex optimization. Mathematical Programming 178:1-2, pages 327-360.
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Nan Ye, Farbod Roosta-Khorasani & Tiangang Cui. 2019. 2017 MATRIX Annals. 2017 MATRIX Annals 121 140 .
Geovani N. Grapiglia & Ekkehard W. Sachs. (2017) On the worst-case evaluation complexity of non-monotone line search algorithms. Computational Optimization and Applications 68:3, pages 555-577.
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E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos & Ph. L. Toint. (2016) Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Mathematical Programming 163:1-2, pages 359-368.
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Katya Scheinberg & Xiaocheng Tang. (2016) Practical inexact proximal quasi-Newton method with global complexity analysis. Mathematical Programming 160:1-2, pages 495-529.
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Elizabeth W. Karas, Sandra A. Santos & Benar F. Svaiter. (2014) Algebraic rules for quadratic regularization of Newton’s method. Computational Optimization and Applications 60:2, pages 343-376.
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Coralia Cartis, Nicholas I. M. Gould & Philippe L. Toint. (2013) On the Evaluation Complexity of Cubic Regularization Methods for Potentially Rank-Deficient Nonlinear Least-Squares Problems and Its Relevance to Constrained Nonlinear Optimization. SIAM Journal on Optimization 23:3, pages 1553-1574.
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