一类推广的非单调拟牛顿算法

A Generalized Non-monotone Quasi-Newton Algorithm

目的为了更有效地利用拟牛顿算法求解无约束优化问题,提高拟牛顿算法的收敛速度,并在数值实验上得到最优解。方法针对拟牛顿方程进行修正,在修正的拟牛顿方程基础上添加参数,利用修正BFGS校正公式,采用非单调线性搜索准则,提出一类新的非单调拟牛顿算法。结果新算法推广了已有的拟牛顿方程,在一定条件下,具有全局收敛性,利用Matlab编制程序对新算法进行数值实验。结论通过数值试验,选取测试函数,得到了最优解。证明了推广的非单调拟牛顿算法是有效的。利用新算法可以更有效地求解无约束优化问题。

Objective To make the quasi-Newton method suitable for solving the non-constrained optimization problems,and improve the convergence speed of this method and get the optimal solution in the numerical experiment.Methods Based on modified quasi-Newton equation with parameters and the BFGS updated,using non-monotone linear search criteria,a new quasi-Newton method with non-monotone is proposed.Results The new algorithm,which has popularized the quasi-Newton method,is verified by numerical experiments programmed in the Matlab language and has global convergence under certain conditions.Conclusions By giving suitable test functions,global optimal solution is found.And it is demonstrated that this approach effectively solves some problems with unconstrained optimization.