快速投影Hessian矩阵算法  

Quick projection method with Hessian matrix

作　　者：汤大林[1] 

机构地区：[1]天津理工大学理学院,天津300191

出　　处：《天津师范大学学报（自然科学版）》2009年第3期18-21,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市高校发展基金项目(20060402)

摘　　要：分析了求解等式约束非线性规划问题的投影Hessian矩阵算法,找出了算法两步Q-超线性收敛的原因,并用BYRD的例子说明此算法的收敛效果较差,即甚至不是线性收敛;对算法进行了合理的改进,并用改进后的算法求解BYRD问题,得到了满意的收敛效果,即Q-超线性收敛.借助数值试验验证了改进算法的快速收敛性.The projection method with Hessian matrix used to solve nonlinear programming with equality constraint is analyzed and the reason why the method is superlinear convergent by two steps is found out. Its bad convergent effect at linearity is illuminated by BYRD＇s example. The method is improved and quickly superlinear convergence of the improved method is illuminated using BYRD＇s example. The quickly convergent effect of the improved method is verified by a numerical experiment.

关 键 词：等式约束非线性规划 投影Hessian矩阵算法 超线性收敛 

分 类 号：O221.2[理学—运筹学与控制论]