改进的混合共轭梯度法求解无约束优化算法  

Improved hybrid conjugate gradient method for unconstrained optimization algorithm

作　　者：吴素芹[1] 於建华[2] 李先锋[1] WU Su-qin YU Jian-hua LI Xian-feng(School of Information Engineering, Yancheng Institute of Technology, Yancheng 224001, China School of Computer Science and Technology, Soochow University, Suzhou 215000, China)

机构地区：[1]盐城工学院信息工程学院,江苏盐城224001 [2]苏州大学计算机科学与技术学院,江苏苏州215000

出　　处：《计算机工程与设计》2017年第8期2155-2160,共6页Computer Engineering and Design

基　　金：国家自然科学基金项目(61105057)

摘　　要：为克服一般的共轭梯度法搜索步长较小、收敛速率慢的不足,提出一种改进的混合共轭梯度算法。引入修正的Armijo线搜索技术,保证该算法的充分下降性,结合拟牛顿法中对Hessen矩阵的近似方法,改进一般共轭梯度法的搜索方向,提高算法的搜索速率,给出该共轭梯度算法的收敛性证明。在标准的无约束优化问题上对该改进共轭梯度算法进行测试,将该算法应用于某化工网络优化模型的求解中,均取得较好的结果。实验结果表明,该共轭梯度算法有较好的收敛速度,有效降低了计算时间。To overcome the problems of the general conjugate gradient method, such that the step length is smaller and the convergence rate is low, an improved hybrid conjugate gradient algorithm was proposed. The corrected Armijo line search techniques were introduced to ensure sufficient descent of the algorithm, and an approximation method for Hessen matrix in quasi-Newton method was used to improve the search direction of the general conjugate gradient method, to improve the search rate of the algorithm. The convergence proof of the conjugate gradient algorithm was provided. The improved conjugate gradient algorithm was tested on a standard unconstrained optimization problem, and the algorithm was applied to solve the optimization model of the chemical network and achieved good results. Results of experiments show that the proposed algorithm has better convergence rate, effectively reducing the computation time.

关 键 词：共轭梯度法 无约束优化 收敛性 修正的Armijo线搜索 Hessen矩阵 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]