中文摘要：

基于非单调技术,本文给出一种新的求解无约束优化的ODE型算法.该算法的特点是：每次迭代时只解一次线性方程组系统而获得试验步,然后采用改进的非单调线搜索获得下一个迭代点,从而避免了重复求解线性方程组,减少了算法的计算量.在合理的假设条件下,该算法被证明是全局收敛和局部超线性收敛的.数值试验证实了该算法的有效性.

英文摘要：

This paper presents a new ODE-based method for unconstrained optimization. A feature of this proposed method is that at each iteration, a system of linear equation system is solved only once to obtain a direction. Then a modified nonmonotone line search along this direction is performed to generate a next point, thus avoiding resolving the linear equation and reducing the amount of calculation. Under some conditions, the global convergence and locally superlinear convergence rate are analyzed. Preliminary numerical results indicate that this algorithm is effective.