On saddle points of a class of augmented Lagrangian functions

Qian Liu; Xinmin Yang; Heung Wing; Heung Wing Joseph Lee

doi:10.3934/jimo.2007.3.693

On saddle points of a class of augmented Lagrangian functions

Qian Liu, Xinmin Yang, Heung Wing, Heung Wing Joseph Lee

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

4 Citations (Scopus)

Abstract

For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.

Original language	English
Pages (from-to)	693-700
Number of pages	8
Journal	Journal of Industrial and Management Optimization
Volume	3
Issue number	4
DOIs	https://doi.org/10.3934/jimo.2007.3.693
Publication status	Published - 1 Jan 2007

Keywords

Augmented Lagrangian function
Nonconvex optimization
Saddle point

ASJC Scopus subject areas

Business and International Management
Strategy and Management
Control and Optimization
Applied Mathematics

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10.3934/jimo.2007.3.693

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title = "On saddle points of a class of augmented Lagrangian functions",

abstract = "For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.",

keywords = "Augmented Lagrangian function, Nonconvex optimization, Saddle point",

author = "Qian Liu and Xinmin Yang and Heung Wing and Lee, {Heung Wing Joseph}",

year = "2007",

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AU - Liu, Qian

AU - Yang, Xinmin

AU - Wing, Heung

AU - Lee, Heung Wing Joseph

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N2 - For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.

AB - For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.

KW - Augmented Lagrangian function

KW - Nonconvex optimization

KW - Saddle point

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U2 - 10.3934/jimo.2007.3.693

DO - 10.3934/jimo.2007.3.693

M3 - Journal article

SN - 1547-5816

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EP - 700

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

IS - 4

ER -

On saddle points of a class of augmented Lagrangian functions

Abstract

Keywords

ASJC Scopus subject areas

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