修正PRP共轭梯度方法求解无约束最优化问题  

Modified PRP conjugate gradient method for unconstrained optimization

作　　者：张慧玲[1] 赛·闹尔再 吴晓云[1] ZHANG Huiling;SAI Naoerzai;WU Xiaoyun(School of Public Education,Bayingol Vocational and Technical College,Korla 841000,Xinjiang,China)

机构地区：[1]巴音郭楞职业技术学院公共教育学院,新疆库尔勒841000

出　　处：《运筹学学报》2022年第2期64-72,共9页Operations Research Transactions

摘　　要：基于著名的PRP共轭梯度方法,利用CGESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。Based on the PRP conjugate gradient method,we propose an efficient modified PRP conjugate gradient method for solving large-scaled unconstrained optimization problems by using the structure of the CGESCENT conjugate gradient method.The proposed method generates a sufficient descent direction at each iteration,which is independent of any line search.Its global convergence and linear convergence rate are established under standard Wolfe line search.The numerical results show that the proposed methods is effective for the given test problems.

关 键 词：无约束最优化 PRP共轭梯度法 WOLFE线搜索 充分下降性 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]