基于三阶拟牛顿方程的对角三阶拟牛顿法

A Diagonal Three-order Quasi-Newton Method Based on Three-order Quasi-Newton Equation

基于三阶拟牛顿方程,结合Zhang H.C.提出的非单调线搜索规则设计了求解大规模无约束优化问题的对角三阶拟牛顿算法。该算法在每次迭代中利用对角矩阵逼近Hessen矩阵的逆,使存储量和计算量明显减少,并且证明了算法的全局收敛性和超线性收敛性。数值试验表明该算法是有效的。

In this paper,we propose a diagonal three-order quasi-Newton method for large-scale unconstrained optimization problems,which is based on three-order quasi-Newton equation and Zhang H.C.non-monotone line search rule.The inverse of Hessen approximation in diagonal matrix form can be obtained,thus avoiding the computational and storing expenses of iterations.The global convergence of the new method is achieved,and the superlinear convergence property is further analyzed.Numerical results show that this method is efficient.