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

2021/08/18 by Jiulin Wang, Mengmeng Song, Wang, Jiulin +3
Mathematics · Computer Science · Engineering · #Advanced Optimization Algorithms Research #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2108.07963

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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