一种放松条件的 Hager-Zhang 共轭梯度算法  

Hanger-Zhang Conjugate Gradient Algorithm for Relaxation Condition

作　　者：赵倩倩 申远[1] ZHAO Qianqian;SHEN Yuan(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210000,China)

机构地区：[1]南京财经大学应用数学学院,江苏南京210000

出　　处：《许昌学院学报》2024年第2期17-21,共5页Journal of Xuchang University

基　　金：国家社会科学基金项目(19AZD018)。

摘　　要：共轭梯度(CG)算法是求解无约束二次优化问题的一种经典算法,但其无法求解非二次问题.为解决该问题,在Hager-Zhang共轭梯度下降算法的基础上引入一个新的参数,设计出一种放松条件的CG下降算法.该算法在每次迭代中不会储存雅可比矩阵,因此能够解决大规模非光滑问题.结果表明,该算法不仅满足全局收敛性且数值表现优异,还可求解单调约束方程.因此它比其他CG算法有更强的适应性.Conjugate gradient(CG)algorithm is a classical algorithm for solving unconstrained quadratic optimization problems,but it can not solve non-quadratic problems.To solve this problem,a new parameter is introduced based on Hager-Zhang conjugate gradient descent algorithm,and a relaxed CG descent algorithm is designed.The algorithm does not store Jacobian matrix in each iteration,so it can solve large-scale non-smooth problems.The results show that the algorithm not only meets the global convergence and has excellent numerical performance,but also can solve the monotone constraint equation.Therefore,it is more adaptable than other CG algorithms.

关 键 词：无约束优化 共轭梯度法 全局收敛性 单调方程 

分 类 号：O224[理学—运筹学与控制论]