Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

Philippe Toint

Namur Institute for Complex Systems

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6 Citations
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2020
Adaptive regularization algorithms with inexact evaluations for nonconvex optimization
Bellavia, S., Gurioli, G., Morini, B. & Toint, P., 2 Jan 2020, In: SIAM Journal on Optimization. 29, 4, p. 2881-2915 35 p.
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2019
Complexity of partially separable convexly constrained optimization with non-Lipschitzian singularities
Chen, X., Toint, P. & Wang, H., 15 Apr 2019, In: SIAM Journal on Optimization. 29, 1, p. 874-903 30 p.
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Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization
Cartis, C., Gould, N. I. M. & Toint, P., 10 Aug 2019, In: Journal of Complexity. 53, p. 68-94 32 p.
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2018
Second-order optimality and beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization
Cartis, C., Gould, N. I. M. & Toint, P., 1 Oct 2018, In: Foundations of Computational Mathematics. 18, 5, p. 1073-1107 35 p.
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2017
Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
Birgin, E. G., Gardenghi, J. L., Martínez, J. M., Santos, S. A. & Toint, P. L., 15 Apr 2017, In: Mathematical Programming. 163, 1-2, p. 359-368 10 p.
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2016
Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models
Birgin, E., Gardenghi, J., Martinez, J-M., Santos, S. & Toint, P., 2016, In: SIAM Journal on Optimization. 26, 2, 20 p.
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2015
On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods
Cartis, C., Gould, N. I. M. & Toint, P. L., 2015, In: SIAM Journal on Numerical Analysis. 53, 2, p. 836-851 16 p.
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Worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization
Cartis, C., Rodrigues Sampaio, P. & Toint, P. L., 4 May 2015, In: Optimization. 64, 5, p. 1349-1361 13 p.
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2014
On the complexity of finding first-order critical points in constrained nonlinear optimization
Cartis, C., Gould, N. I. M. & Toint, P. L., 2014, In: Mathematical Programming. 144, 1-2, p. 93-106 14 p.
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2013
A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function
Cartis, C., Gould, N. I. M. & Toint, P. L., 1 Jun 2013, In: Optimization Methods and Software. 28, 3, p. 451-457 7 p.
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On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization
Cartis, C., Gould, N. & Toint, P., 29 Oct 2013, In: SIAM Journal on Optimization. 23, 3, p. 1553-1574 22 p.
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2012
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
Cartis, C., Gould, N. & Toint, P., 1 Oct 2012, In: IMA Journal of Numerical Analysis. 32, 4, p. 1662-1695 34 p.
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Complexity bounds for second-order optimality in unconstrained optimization
Cartis, C., Gould, N. I. M. & Toint, P., 1 Feb 2012, In: Journal of Complexity. 28, p. 93-108 16 p.
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Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
Toint, P., Cartis, C. & Gould, N., 1 Apr 2012, In: Optimization Methods and Software. 27, 2, p. 197-219 23 p.
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How much patience do you have? A worst-case perspective on smooth nonconvex optimization
Cartis, C., Gould, N. & Toint, P., 1 Jan 2012, In: Optima. 88, 1-10
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On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization
Cartis, C., Gould, N. I. M. & Toint, P., 1 Jan 2012, In: SIAM Journal on Optimization. 22, 1, p. 66-86 21 p.
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Updating the regularization parameter in the adaptive cubic regularization algorithm
Gould, N., Porcelli, M. & Toint, P., 1 Sept 2012, In: Computational Optimization and Applications. 53, 1, p. 1-22 22 p.
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2011
Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results
Cartis, C., Gould, N. I. M. & Toint, P. L., 1 Apr 2011, In: Mathematical Programming. 127, 2, p. 245-295 51 p.
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Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity
Cartis, C., Gould, N. & Toint, P., 1 Dec 2011, In: Mathematical Programming. 130, 2, p. 295-319 25 p.
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2010
On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization problems
Cartis, C., Gould, N. & Toint, P., 1 Jan 2010, In: SIAM Journal on Optimization. 20, 6, p. 2833-2852 20 p.
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Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

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