有界变量约束优化的仿射投影共轭梯度路径内点方法  

An affine scaling interior projected conjugate gradient path algorithm for the box constrained optimization

作　　者：林涛[1] 朱德通[1] 

机构地区：[1]上海师范大学数理信息学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2005年第3期11-16,共6页Journal of Shanghai Normal University(Natural Sciences)

基　　金：上海市科委自然科学基金资助项目(02ZA14070).

摘　　要：采用共轭梯度路径结合仿射内点投影回代技术解有界变量约束的非线性优化问题.通过构造共轭梯度路径解二次模型获得搜索方向,引入线搜索技术获得的迭代步既落在严格可行域内,又能使目标函数下降.基于共轭梯度路径的性质,在合理的假设条件下,证明了所提供的算法不仅具有整体收敛性,而且保持快速的超线性收敛速率.进一步,数值计算说明了算法的可行性和有效性.Proposes an affine scaling projected conjugate gradient path algorithm with interior back - tracking technique for the nonlinear optimization subject to bounds on variables. Employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the quadratic model. Using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function monotonically decreasing. Theoretical analysis proves that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. Furthermore, numerical results indicate that the algorithm is effective.

关 键 词：有界变量约束 共轭梯度路径 内点法 仿射投影 

分 类 号：O221.2[理学—运筹学与控制论]