带有延迟步长的循环BB梯度法  

Cyclic Barzilai-Borwein Gradient Method with Retards Step-size

作　　者：杨奕涵 YANG Yihan(School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《东莞理工学院学报》2024年第1期1-6,共6页Journal of Dongguan University of Technology

摘　　要：梯度法是求解大规模无约束优化问题的常用方法。将求解二次函数极小化问题的步长推广至一般无约束优化问题,通过使用延迟一步以及循环梯度法的思想,提出了循环Barzilai-Borwein梯度法(BB梯度法),并结合Zhang-Hager非单调线搜索技术,给出了求解一般无约束优化问题的循环BB梯度算法—CBBGM算法。在适当的假设下,CBBGM算法是全局收敛的,且目标函数为强凸函数时,该算法具有线性收敛速度。数值试验表明,与现有的方法相比,所提出的方法在计算上更高效。Gradient method is a common method for solving large scale unconstrained optimization problems.In this paper,the step size of solving quadratic function minimization problem is extended to solving general unconstrained optimization problem.By using the idea of one-step retard and cyclic gradient method,the cyclic BB gradient method is proposed,and combined with the Zhang-Hager non-monotonic line search technique,A cyclic BB gradient algorithm-CBBGM algorithm is presented for solving general unconstrained optimization problems.Under suitable assumptions,the CBBGM algorithm has global convergence and linear convergence rate when the objective function is strongly convex.Numerical experiments show that the proposed method is more computationally efficient than the existing methods.

关 键 词：Barzilai-Borwein梯度法 无约束优化问题 Zhang-Hager非单调线搜索 全局收敛性 

分 类 号：O241[理学—计算数学]