A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization

Richard H. Byrd; Jorge Nocedal

doi:10.1137/0726042

A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization

Richard H. Byrd, Jorge Nocedal

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The BFGS update formula is shown to have an important property that is independent of the algorithmic context of the update, and that is relevant to both constrained and unconstrained optimization. The BFGS method for unconstrained optimization, using a variety of line searches, including backtracking, is shown to be globally and superlinearly convergent on uniformly convex problems. The analysis is particularly simple due to the use of some new tools introduced in this paper.

Original language	English
Pages (from-to)	727-739
Journal	SIAM Journal on Numerical Analysis
Volume	26
DOIs	https://doi.org/10.1137/0726042
State	Published - Jun 1989

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title = "A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization",

abstract = "The BFGS update formula is shown to have an important property that is independent of the algorithmic context of the update, and that is relevant to both constrained and unconstrained optimization. The BFGS method for unconstrained optimization, using a variety of line searches, including backtracking, is shown to be globally and superlinearly convergent on uniformly convex problems. The analysis is particularly simple due to the use of some new tools introduced in this paper.",

author = "Byrd, {Richard H.} and Jorge Nocedal",

year = "1989",

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AB - The BFGS update formula is shown to have an important property that is independent of the algorithmic context of the update, and that is relevant to both constrained and unconstrained optimization. The BFGS method for unconstrained optimization, using a variety of line searches, including backtracking, is shown to be globally and superlinearly convergent on uniformly convex problems. The analysis is particularly simple due to the use of some new tools introduced in this paper.

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DO - 10.1137/0726042

M3 - Article

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VL - 26

SP - 727

EP - 739

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

ER -

A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization

Abstract

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