求解无约束函数局部鞍点的数值算法

Numerical algorithm for solving local saddle points of unconstrained functions

该文利用无约束优化问题的最优性条件,首先提了一种在给定区域内求解函数的局部鞍点的数值算法.接着根据局部鞍点和全局鞍点的关系,提出了验证局部鞍点是否为全局鞍点的数值算法.然后对两个算法进行了收敛性分析.最后通过数值实验验证了两个数值算法的有效性.

In this paper,we propose a numerical algorithm for solving the local saddle point in a given region by using the optimality condition of unconstrained optimization problems.Furthermore,according to the relationship between the local saddle point and the global saddle point,we propose a numerical algorithm to verify whether local saddle points are global saddle points.Then the convergences of the two proposed algorithms are proved.Finally,some numerical examples are provided to illustrate validity of these algorithms.