A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization

Andreas Fischer; Pradyumn K. Shukla

doi:10.1016/j.orl.2008.02.006

A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization

Andreas Fischer^*, Pradyumn K. Shukla

^*Corresponding author for this work

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Technische Universitat Dresden

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

Abstract

To compute one of the nonisolated Pareto-critical points of an unconstrained multicriteria optimization problem a Levenberg-Marquardt algorithm is applied. Sufficient conditions for an error bound are provided to prove its fast local convergence. A globalized version is shown to converge to a Pareto-optimal point under convexity assumptions.

Original language	English
Pages (from-to)	643-646
Number of pages	4
Journal	Operations Research Letters
Volume	36
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2008.02.006
Publication status	Published - Sept 2008

Keywords

Error bound
Levenberg-Marquardt method
Multicriteria optimization
Quadratic convergence

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10.1016/j.orl.2008.02.006

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title = "A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization",

abstract = "To compute one of the nonisolated Pareto-critical points of an unconstrained multicriteria optimization problem a Levenberg-Marquardt algorithm is applied. Sufficient conditions for an error bound are provided to prove its fast local convergence. A globalized version is shown to converge to a Pareto-optimal point under convexity assumptions.",

keywords = "Error bound, Levenberg-Marquardt method, Multicriteria optimization, Quadratic convergence",

author = "Andreas Fischer and Shukla, {Pradyumn K.}",

year = "2008",

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AU - Shukla, Pradyumn K.

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N2 - To compute one of the nonisolated Pareto-critical points of an unconstrained multicriteria optimization problem a Levenberg-Marquardt algorithm is applied. Sufficient conditions for an error bound are provided to prove its fast local convergence. A globalized version is shown to converge to a Pareto-optimal point under convexity assumptions.

AB - To compute one of the nonisolated Pareto-critical points of an unconstrained multicriteria optimization problem a Levenberg-Marquardt algorithm is applied. Sufficient conditions for an error bound are provided to prove its fast local convergence. A globalized version is shown to converge to a Pareto-optimal point under convexity assumptions.

KW - Error bound

KW - Levenberg-Marquardt method

KW - Multicriteria optimization

KW - Quadratic convergence

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DO - 10.1016/j.orl.2008.02.006

M3 - Article

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SP - 643

EP - 646

JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

ER -

A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization

Abstract

Keywords

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