On Local Nonglobal Minimum of Trust-Region Subproblem and Extension

Jiulin Wang; Mengmeng Song; Yong Xia

doi:10.1007/s10957-022-02115-x

On Local Nonglobal Minimum of Trust-Region Subproblem and Extension

Jiulin Wang
, Mengmeng Song
, Yong Xia^*

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

The local nonglobal minimizer of the trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is extended to the p-regularized subproblem. As a corollary, we show for the first time that finding the local nonglobal minimizer of the Nesterov–Polyak subproblem corresponds to a generalized eigenvalue problem.

Original language	English
Pages (from-to)	707-722
Number of pages	16
Journal	Journal of Optimization Theory and Applications
Volume	195
Issue number	2
DOIs	https://doi.org/10.1007/s10957-022-02115-x
State	Published - Nov 2022

Keywords

Local nonglobal minimizer
Nesterov–Polyak subproblem
Trust-region subproblem
p-regularized subproblem

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10.1007/s10957-022-02115-x

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abstract = "The local nonglobal minimizer of the trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is extended to the p-regularized subproblem. As a corollary, we show for the first time that finding the local nonglobal minimizer of the Nesterov–Polyak subproblem corresponds to a generalized eigenvalue problem.",

keywords = "Local nonglobal minimizer, Nesterov–Polyak subproblem, Trust-region subproblem, p-regularized subproblem",

author = "Jiulin Wang and Mengmeng Song and Yong Xia",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s10957-022-02115-x",

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AU - Xia, Yong

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Y1 - 2022/11

N2 - The local nonglobal minimizer of the trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is extended to the p-regularized subproblem. As a corollary, we show for the first time that finding the local nonglobal minimizer of the Nesterov–Polyak subproblem corresponds to a generalized eigenvalue problem.

AB - The local nonglobal minimizer of the trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is extended to the p-regularized subproblem. As a corollary, we show for the first time that finding the local nonglobal minimizer of the Nesterov–Polyak subproblem corresponds to a generalized eigenvalue problem.

KW - Local nonglobal minimizer

KW - Nesterov–Polyak subproblem

KW - Trust-region subproblem

KW - p-regularized subproblem

UR - https://www.scopus.com/pages/publications/85139192487

U2 - 10.1007/s10957-022-02115-x

DO - 10.1007/s10957-022-02115-x

M3 - 文章

AN - SCOPUS:85139192487

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EP - 722

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -

On Local Nonglobal Minimum of Trust-Region Subproblem and Extension

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Keywords

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