改进的混合共轭梯度法求解无约束优化算法

摘要

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.%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.