2026 年 17 巻 3 号 p. 896-911
This paper proposes the Inertial Cubic regularized Newton (ICN) method, which incorporates inertial terms into the Cubic regularized Newton (CN) framework to accelerate convergence while preserving numerical stability. With the rapid growth of data-driven applications, conventional Newton-type methods have increasingly suffered from instability caused by indefinite or ill-conditioned Hessian matrices. The CN method addresses these issues by employing cubic regularization, ensuring global convergence to stationary points under standard assumptions and improved robustness. However, its convergence speed can still be limited in practice. To overcome this limitation, the proposed ICN method introduces inertial terms, originally developed for accelerating first-order optimization methods, into the second-order CN framework. This integration enhances convergence efficiency without compromising solution accuracy or stability. The effectiveness of the proposed method is demonstrated through extensive computational experiments on benchmark function optimization, logistic regression, and pattern classification problems. The results show that the ICN method consistently achieves faster convergence and improved robustness compared to existing second-order optimization algorithms.
