有界约束非线性优化问题的仿射共轭梯度路径法  

AN AFFINE SCALING CONJUGATE GRADIENT PATH METHOD FOR NONLINEAR OPTIMIZATION SUBJECT TO BOUNDS

作　　者：鲍吉锋[1] 朱德通[2] 

机构地区：[1]浙江大学数学系,杭州310027 [2]上海师范大学商学院,上海200234

出　　处：《计算数学》2009年第1期37-50,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(编号10871130);博士点基金项目(编号0527003);上海市重点学科项目(编号T0401);上海市教委项目(编号05DZ11)资助.

摘　　要：本文提出仿射内点离散共轭梯度路径法解有界约束的非线性优化问题.通过构造预条件离散的共轭梯度路径解二次模型获得预选迭代方向,结合内点回代线搜索获得下一步的迭代.在合理的假设条件下,证明了算法的整体收敛性与局部超线性收敛速率.最后,数值结果表明了算法的有效性.In this paper, we propose a new approach of affine scaling interior discrete conjugate gradient path for solving bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via constructing preconditioned conjugate gradient path. By combining interior backtracking line search, we obtain the next iteration. Global convergence and local superlinear convergence rate of the proposed algorithm are established on some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

关 键 词：共轭梯度 预条件 仿射变换 线搜索 

分 类 号：O224[理学—运筹学与控制论] O221.2[理学—数学]