曲线搜索下新的记忆拟牛顿算法

A New Memory Quasi-Newton Method with Curve Search Rule

利用新的曲线搜索方法,提出一种解决无约束优化问题的记忆拟牛顿算法,给出该算法全局收敛的条件并进行数值实验.新算法由曲线搜索确定迭代步长,搜索方向用到当前迭代点信息的同时还用到上一次迭代点的信息,而且搜索方向与迭代步长同时确定,是一种有效的算法.

By means of a new curve search rule ,we propose a new memory quasi-Newton method for unconstrained optimization problems. A global convergent result is proved and numerical experiments are carried out. The step-size of the new algorithm is determined by the new curve search rule. The search direction not only make use of the current iterative information but also the previous kerative information. Moreover, the search direction and the step-size are determined simultaneously at each iteration. Numerical results show that the algorithm is effective.