Trust-region and $p$-regularized subproblems: local nonglobal minimum is the second smallest objective function value among all first-order stationary points
Optimization and Control
2021-08-19 v1
Abstract
The local nonglobal minimizer of 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 -regularized subproblem. As a corollary, we show for the first time that finding the local nonglobal minimizer of Nesterov-Polyak subproblem corresponds to a generalized eigenvalue problem.
Keywords
Cite
@article{arxiv.2108.07963,
title = {Trust-region and $p$-regularized subproblems: local nonglobal minimum is the second smallest objective function value among all first-order stationary points},
author = {Jiulin Wang and Mengmeng Song and Yong Xia},
journal= {arXiv preprint arXiv:2108.07963},
year = {2021}
}
Comments
13 pages, 1 figure