Generalized Levitin-polyak well-posedness in constrained optimization

X. X. Huang; Xiaoqi Yang

doi:10.1137/040614943

Generalized Levitin-polyak well-posedness in constrained optimization

X. X. Huang, Xiaoqi Yang

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

103 Citations (Scopus)

Abstract

In this paper, we consider Levitin-Polyak-type well-posedness for a general constrained optimization problem. We introduce generalized Levitin-Polyak well-posedness and strongly generalized Levitin-Polyak well-posedness. Necessary and sufficient conditions for these types of well-posedness are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods and a class of augmented Lagrangian methods under the assumption of strongly generalized Levitin-Polyak well-posedness.

Original language	English
Pages (from-to)	243-258
Number of pages	16
Journal	SIAM Journal on Optimization
Volume	17
Issue number	1
DOIs	https://doi.org/10.1137/040614943
Publication status	Published - 26 Feb 2007

Keywords

Constrained optimization
Generalized Levitin-Polyak well-posedness
Generalized minimizing sequence
Penalty-type methods

ASJC Scopus subject areas

Theoretical Computer Science
Software

More information

10.1137/040614943

http://hdl.handle.net/10397/6099

Cite this

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AB - In this paper, we consider Levitin-Polyak-type well-posedness for a general constrained optimization problem. We introduce generalized Levitin-Polyak well-posedness and strongly generalized Levitin-Polyak well-posedness. Necessary and sufficient conditions for these types of well-posedness are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods and a class of augmented Lagrangian methods under the assumption of strongly generalized Levitin-Polyak well-posedness.

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KW - Generalized minimizing sequence

KW - Penalty-type methods

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Generalized Levitin-polyak well-posedness in constrained optimization

Abstract

Keywords

ASJC Scopus subject areas

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