Globally convergent inexact generalized Newton method for first-order differentiable optimization problems

D. Pu; J. Zhang

doi:10.1023/A:1004605428858

Globally convergent inexact generalized Newton method for first-order differentiable optimization problems

D. Pu
, J. Zhang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

Motivated by the method of Martinez and Qi (Ref. 1), we propose in this paper a globally convergent inexact generalized Newton method to solve unconstrained optimization problems in which the objective functions have Lipschitz continuous gradient functions, but are not twice differentiable. This method is implementable, globally convergent, and produces monotonically decreasing function values. We prove that the method has locally superlinear convergence or even quadratic convergence rate under some mild conditions, which do not assume the convexity of the functions.
© 2000 Plenum Publishing Corporation

Original language	English
Pages (from-to)	551-568
Journal	Journal of Optimization Theory and Applications
Volume	106
Issue number	3
DOIs	https://doi.org/10.1023/A:1004605428858
Publication status	Published - Sept 2000
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

This research was supported by the Hong Kong Research Grant Council, Competitive Earmarked Research Grant CITYU-9040289.

Research Keywords

Generalized Newton methods
Global convergence
Inexact Newton methods
Nonsmooth optimization
Superlinear rate

RGC Funding Information

RGC-funded

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title = "Globally convergent inexact generalized Newton method for first-order differentiable optimization problems",

abstract = "Motivated by the method of Martinez and Qi (Ref. 1), we propose in this paper a globally convergent inexact generalized Newton method to solve unconstrained optimization problems in which the objective functions have Lipschitz continuous gradient functions, but are not twice differentiable. This method is implementable, globally convergent, and produces monotonically decreasing function values. We prove that the method has locally superlinear convergence or even quadratic convergence rate under some mild conditions, which do not assume the convexity of the functions. {\textcopyright} 2000 Plenum Publishing Corporation",

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TY - JOUR

T1 - Globally convergent inexact generalized Newton method for first-order differentiable optimization problems

AU - Pu, D.

AU - Zhang, J.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2000/9

Y1 - 2000/9

N2 - Motivated by the method of Martinez and Qi (Ref. 1), we propose in this paper a globally convergent inexact generalized Newton method to solve unconstrained optimization problems in which the objective functions have Lipschitz continuous gradient functions, but are not twice differentiable. This method is implementable, globally convergent, and produces monotonically decreasing function values. We prove that the method has locally superlinear convergence or even quadratic convergence rate under some mild conditions, which do not assume the convexity of the functions. © 2000 Plenum Publishing Corporation

AB - Motivated by the method of Martinez and Qi (Ref. 1), we propose in this paper a globally convergent inexact generalized Newton method to solve unconstrained optimization problems in which the objective functions have Lipschitz continuous gradient functions, but are not twice differentiable. This method is implementable, globally convergent, and produces monotonically decreasing function values. We prove that the method has locally superlinear convergence or even quadratic convergence rate under some mild conditions, which do not assume the convexity of the functions. © 2000 Plenum Publishing Corporation

KW - Generalized Newton methods

KW - Global convergence

KW - Inexact Newton methods

KW - Nonsmooth optimization

KW - Superlinear rate

UR - https://www.scopus.com/pages/publications/0034336668

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0034336668&origin=recordpage

U2 - 10.1023/A:1004605428858

DO - 10.1023/A:1004605428858

M3 - RGC 21 - Publication in refereed journal

SN - 0022-3239

VL - 106

SP - 551

EP - 568

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Globally convergent inexact generalized Newton method for first-order differentiable optimization problems

Abstract

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Research Keywords

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