中文摘要：

提出了一种新的求解无约束优化问题的ODE型方法，其特点是：它在每次迭代时仅求解一个线性方程组系统来获得试探步；若该试探步不被接受，算法就沿着该试探步的方向求得下一个迭代点，其中步长通过固定公式计算得到．这样既避免了传统的ODE型算法中为获得可接受的试探步而重复求解线性方程组系统，又不必执行线搜索，从而减少了计算量．在适当的条件下，还证明了新算法的整体收敛性和局部超线性收敛性．数值试验结果表明：提出的算法是有效的．

英文摘要：

In this paper, a new ODE-based method is proposed for solving unconstrained optimization problems. It obtains a trial step only by solving a linear equation system in each iteration. If the trial step cannot be accepted, the algorithm acquires the next iterative point along the direction of the trial step, in which the step is determined by a fixed formula. In this way, we not only avoid resolving the linear equation system repeatedly to obtain an acceptable trial step, but also reduce the amount of calculation without performing line search. The globally convergence and locally superlinear convergence of the algorithm will be established under some favorable conditions. And preliminary numerical results show that the new algorithm is effective.