A Newton-CG algorithm with complexity guarantees for smooth unconstrained optimization

• 成果类型: Article
• 署名作者: Royer, Clement W.; O'Neill, Michael; Wright, Stephen J.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01362-7
• 发表日期: 2020
• 页码: 451-488
• 关键词: cubic-regularization; descent

摘要

We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the Hessian of the objective function. The algorithm tracks Newton-conjugate gradient procedures developed in the 1980s closely, but includes enhancements that allow worst-case complexity results to be proved for convergence to points that satisfy approximate first-order and second-order optimality conditions. The complexity results match the best known results in the literature for second-order methods.