On superlinear convergence of quasi-Newton methods for nonsmooth equations

Liqun Qi

On superlinear convergence of quasi-Newton methods for nonsmooth equations

Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.

Original language	English
Pages (from-to)	223-228
Number of pages	6
Journal	Operations Research Letters
Volume	20
Issue number	5
Publication status	Published - 1 Jun 1997
Externally published	Yes

Keywords

Nonsmooth equations
Quasi-Newton methods
Superlinear convergence
The Broyden method

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

Cite this

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title = "On superlinear convergence of quasi-Newton methods for nonsmooth equations",

abstract = "We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.",

keywords = "Nonsmooth equations, Quasi-Newton methods, Superlinear convergence, The Broyden method",

author = "Liqun Qi",

year = "1997",

month = jun,

day = "1",

language = "English",

volume = "20",

pages = "223--228",

journal = "Operations Research Letters",

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publisher = "Elsevier B.V.",

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TY - JOUR

T1 - On superlinear convergence of quasi-Newton methods for nonsmooth equations

AU - Qi, Liqun

PY - 1997/6/1

Y1 - 1997/6/1

N2 - We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.

AB - We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.

KW - Nonsmooth equations

KW - Quasi-Newton methods

KW - Superlinear convergence

KW - The Broyden method

UR - https://www.scopus.com/pages/publications/0000021390

M3 - Journal article

SN - 0167-6377

VL - 20

SP - 223

EP - 228

JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

ER -

On superlinear convergence of quasi-Newton methods for nonsmooth equations

Abstract

Keywords

ASJC Scopus subject areas

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