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arXiv · 2108.07963

Trust-region and $p$-regularized subproblems: local nonglobal minimum is the second smallest objective function value among all first-order stationary points

Jiulin Wang·Mengmeng Song·Yong Xia
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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 $p$-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.

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Jiulin Wang, Mengmeng Song, Yong Xia. 2021-08-18. Trust-region and $p$-regularized subproblems: local nonglobal minimum is the second smallest objective function value among all first-order stationary points. https://arxiv.org/abs/2108.07963

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