CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

• 来源期刊: 计算数学(英文版)
• 学科: 数学
• 关键词: Curvilinear paths Trust region methods Nonmonotonic technique Unconstrained optimization.
• 年，卷（期）: 2001,（3）
• 页码范围: 241-258
• 页数: 18页
• 分类号: O1
• 语种: 英文

摘要

In this paper we modify type approximate trust region methods via two curvilinear paths for unconstrained optimization. A mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We give a series of properties of both optimal path and modified gradient path. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases.