TY - JOUR
T1 - On Local Nonglobal Minimum of Trust-Region Subproblem and Extension
AU - Wang, Jiulin
AU - Song, Mengmeng
AU - Xia, Yong
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/11
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
SN - 0022-3239
VL - 195
SP - 707
EP - 722
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -