Newton-CG Methods for Nonconvex Unconstrained Optimization with Holder Continuous Hessian

• 成果类型: Article; Early Access
• 署名作者: He, Chuan; Huang, Heng; Lu, Zhaosong
• 署名单位: Linkoping University; University System of Maryland; University of Maryland College Park; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0356
• 发表日期: 2025
• 关键词: cubic-regularization; Gradient descent; complexity; POWER; algorithms

摘要

In this paper, we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with Holder continuous Hessian. Specifically, we first propose a Newton-conjugate gradient (Newton-CG) method for finding an approximate firstand second-order stationary point of this problem, assuming the associated Holder parameters are explicitly known. Then, we develop a parameter-free Newton-CG method without requiring any prior knowledge of these parameters. To the best of our knowledge, this method is the first parameter-free second-order method achieving the best-known iteration and operation complexity for finding an approximate firstand second-order stationary point of this problem. Finally, we present preliminary numerical results to demonstrate the superior practical performance of our parameter-free Newton-CG method over a well-known regularized Newton method.