An Unregularized Third Order Newton Method

2022/09/21 by Olha Silina, Silina, Olha, Jeffrey Zhang +1 · 1 citation
Computer Science · Mathematics · #49M15 #65K05 #90C22 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Methods and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2209.10051

openalex publication_date 2022/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a third-order Newton's method which in each iteration solves a semidefinite program as a subproblem. Our approach is based on moving to the local minimum of the third-order Taylor expansion at each iteration, rather than that of the second order. We show that this scheme has local cubic convergence. We then provide numerical experiments comparing this scheme to some standard algorithms.

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