| 朱德通.非单调技术预条件弧线路径信赖域解无约束优化(英文)[J].数学研究及应用,2004,24(4):627~648 |
| 非单调技术预条件弧线路径信赖域解无约束优化(英文) |
| Curvilinear Paths with Nonmonotonic Inexact Line Search Technique for Unconstrained Optimization |
| 投稿时间：2002-03-11 |
| DOI：10.3770/j.issn:1000-341X.2004.04.008 |
| 中文关键词: 弧线路径 预条件因子 信赖域 非单调技术 |
| 英文关键词:Curvilinear paths preconditioned trust region methods nonmonotonic technique. |
| 基金项目: |
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| 摘要点击次数: 2318 |
| 全文下载次数: 1300 |
| 中文摘要: |
| 本文提供修正近似信赖域类型路经三类预条件弧线路径方法解无约束最优化问题.使用对称矩阵的稳定Bunch-Parlett易于形成信赖域子问题的弧线路径,使用单位下三角矩阵作为最优路径和修正梯度路径的预条件因子.运用预条件因子改进Hessian矩阵特征值分布加速预条件共轭梯度路径收敛速度.基于沿着三类路径信赖域子问题产生试探步,将信赖域策略与非单调线搜索技术相结合作为新的回代步.理论分析证明在合理条件下所提供的算法是整体收敛性,并且具有局部超线性收敛速率,数值结果表明算法的有效性. |
| 英文摘要: |
| In this paper we modify approximate trust region methods via three preconditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent,we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local superlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms. |
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