A trust region algorithm with a worst-case iteration complexity of O(ϵ-3/2) for nonconvex optimization

We propose a trust region algorithm for solving nonconvex smooth optimization problems. For any ϵ ¯ ∈ ( 0 , ∞ ) , the algorithm requires at most O ( ϵ - 3 / 2 ) iterations, function evaluations, and derivative evaluations to drive the norm of the gradient of the objective function below any ϵ ∈ ( 0...

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Bibliographic Details
Published in:	Mathematical programming Vol. 162; no. 1-2; pp. 1 - 32
Main Authors:	Curtis, Frank E., Robinson, Daniel P., Samadi, Mohammadreza
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017 Springer Nature B.V
Subjects:	Applied mathematics Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization algorithms Regularization methods Theoretical 58C15 68Q25 Global convergence Worst-case iteration complexity Unconstrained optimization Nonconvex optimization 65K05 Nonlinear optimization 65Y20 90C30 65K10 49M15 49M37 Local convergence 90C60 Trust region methods Worst-case evaluation complexity
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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