Combining and scaling descent and negative curvature directions

• 成果类型: Article
• 署名作者: Avelino, Catarina P.; Moguerza, Javier M.; Olivares, Alberto; Prieto, Francisco J.
• 署名单位: University of Tras-os-Montes & Alto Douro; Universidad Rey Juan Carlos; Universidad Carlos III de Madrid
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0305-6
• 发表日期: 2011
• 页码: 285-319
• 关键词: conjugate-gradient method; minimization; optimization; search

摘要

The aim of this paper is the study of different approaches to combine and scale, in an efficient manner, descent information for the solution of unconstrained optimization problems. We consider the situation in which different directions are available in a given iteration, and we wish to analyze how to combine these directions in order to provide a method more efficient and robust than the standard Newton approach. In particular, we will focus on the scaling process that should be carried out before combining the directions. We derive some theoretical results regarding the conditions necessary to ensure the convergence of combination procedures following schemes similar to our proposals. Finally, we conduct some computational experiments to compare these proposals with a modified Newton's method and other procedures in the literature for the combination of information.