SIAM Journal on Optimization, Volume 30, Issue 4, Page 3345-3358, January 2020.
Cubic regularization methods have several favorable properties. In particular under mild assumptions, they are globally convergent towards critical points with second-order necessary conditions satisfied. Their adoption among practitioners, however, does not yet match the strong theoretical results. One of the reasons for this discrepancy may be the additional implementation complexity needed to solve the cubic regularization subproblems. In this paper we show that this complexity can be decreased significantly by reducing the subproblem to a generalized eigenvalue problem. The resulting algorithm is not only robust, due to existing highly advanced eigenvalue solvers, but also provides a new way of employing second-order methods in the large-scale case.

中文翻译：

---

用广义特征值问题解决大规模三次正则化问题

SIAM优化杂志，第30卷，第4期，第3345-3358页，2020年1月。
三次正则化方法具有几个有利的属性。特别是在温和的假设下，它们已在满足二阶必要条件的情况下趋向临界点。然而，它们在实践者中的采用尚不符合强有力的理论结果。这种差异的原因之一可能是解决三次正则化子问题所需的其他实现复杂性。在本文中，我们表明可以通过将子问题减少为广义特征值问题来显着降低这种复杂性。由于现有高度先进的特征值求解器，所得算法不仅鲁棒性强，而且在大规模情况下提供了一种采用二阶方法的新方法。