简单界约束非线性方程组的不精确线搜索法

Nonmonotone Line Search Method for Nonlinear Equations with Simple Bounds

提出一种用非单调线搜索方法求解简单界约束非线性方程组,算法采用满足Armijo条件的不精确线搜索技巧,并使用非单调结构,将当前函数最大值的下降改进为函数平均值的下降,推广了算法的适用范围.最后进行了数值试验,结果表明,算法十分有效.

In this paper we present a nonmonotone line search method for solving nonlinear equations with simple bounds. The new method uses inaccuracy line search technique which satisfies Armijo conditions, and uses normaotone structure which relaxes the conditions that the trial step is accepted. The ＂max＂ of function values is replaced by an average of function values. The new method is more concise and more general. Under the standard assumptions, the global convergence for the algorithm is proven. Finally, the numerical test report is given which shows the new method is very effective.