On Local Nonglobal Minimum of Trust-Region Subproblem and Extension

Jiulin Wang (), Mengmeng Song () and Yong Xia ()
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Jiulin Wang: Fudan University
Mengmeng Song: Beihang University
Yong Xia: Beihang University

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 15, 707-722

Abstract: 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: Trust-region subproblem; p-regularized subproblem; Nesterov–Polyak subproblem; Local nonglobal minimizer; 90C20; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02115-x

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