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

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

An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, DAMTP, University of Cambridge), an algorithm by Nesterov and Polyak (Math Program 108(1):177-205, 20...

Disgrifiad llawn

Manylion Llyfryddiaeth
Prif Awduron:	Cartis, C, Gould, N, Toint, P
Fformat:	Journal article
Iaith:	English
Cyhoeddwyd:	2011

Eitemau Tebyg

Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity.
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Adaptive cubic overestimation methods for unconstrained optimization
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Adaptive cubic overestimation methods for unconstrained optimization
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Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization.
gan: Cartis, C, et al.
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Complexity bounds for second-order optimality in unconstrained optimization.
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Trust-region and other regularisations of linear least-squares problems
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Trust-region and other regularisations of linear least-squares problems
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On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems.
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Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
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An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
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A concise second-order complexity analysis for unconstrained optimization using high-order regularized models
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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
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Global convergence rate analysis of unconstrained optimization methods based on probabilistic models
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Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
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Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares.
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Second-order optimality and beyond: characterization and evaluation complexity in convexly-constrained nonlinear optimization
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On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods
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Numerical methods for unconstrained optimization/
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On the complexity of finding first-order critical points in constrained nonlinear optimization
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Corrigendum: On the complexity of finding first-order critical points in constrained nonlinear optimization
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Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints
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On solving trust−region and other regularised subproblems in optimization
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Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
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Convergence and stability of line search methods for unconstrained optimization.
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On solving trust-region and other regularised subproblems in optimization
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Numerical methods for unconstrained optimization : an introduction/
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Universal regularization methods: varying the power, the smoothness and the accuracy
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Global convergence of conjugate gradient method in unconstrained optimization problems
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Adaptive regularization with cubics on manifolds
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Numerical methods for unconstrained optimization and nonlinear equations/
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A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality
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Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
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On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming.
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On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization.
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A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function.
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Fuzzy adaptive teaching learning-based optimization for solving unconstrained numerical optimization problems
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The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization
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A Modified Conjugate Gradient Method with Global Convergence Property for Unconstrained Optimization
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An Improved Adaptive Trust-Region Method for Unconstrained Optimization
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Adaptive Cuckoo Search Algorithm for Unconstrained Optimization
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