On Local Nonglobal Minimum of Trust-Region Subproblem and Extension

Jiulin Wang, Mengmeng Song, Yong Xia

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.