一类新的基于信赖域技术的非单调共轭梯度算法

A New Non-monotone Conjugate Gradient Method Based on the Trust Region Technique

为有效求解大规模无约束优化问题,本文基于信赖域技术和修正拟牛顿方程,同时结合Zhang H.C.策略和Gu N.Z.策略,设计了一种新的非单调共轭梯度算法,应用信赖域技术保证了算法的稳健性和收敛性,并给出了算法的全局收敛性分析.在适当条件下,证明了该算法具有线性收敛性.数值实验表明新算法能够有效求解病态和大规模问题.与单独结合其中一种非单调策略的算法相比,新算法需要较少的迭代次数和运行时间,利用其得到的函数值与最优值更接近.

In order to effectively solve the large-scale unconstrained optimization problem,based on the trust region technique and the modified quasi-Newton equation,a new nonmonotone conjugate gradient algorithm is presented by combining Zhang H.C.and Gu N.Z.strategy in this paper.The trust region technique is applied to ensure the robustness and convergence of the algorithm,and the global convergence property of the algorithm is also analyzed.Under some reasonable conditions,it is proved that the proposed algorithm is linear convergent.Numerical examples indicate that the new algorithm can effectively solve ill-conditioned and large-scale problems.Compared with the algorithm that combines one of the non-monotonic strategies,the new algorithm requires fewer iteration numbers and less running time,and the function value obtained by the new algorithm is closer to the optimal value.