基于F-B函数的牛顿法解一般约束优化规划问题

文章给出了一个解决一般约束最优化问题的含调节参数型的牛顿算法.算法有两个重要特征,首先,算法借助Lagrange函数和NcP中的F-B函数,通过构造等价于点条件的线性方程组采处理一般约束优化问题,其次,利用F-B函数的光滑性质,定义了调节参数,从而弱化了K-T点条件.文章在适当的条件下,证明了该算法具有全局收敛性.数值实验表明算法有效.

A Newton Algorithm with F-B Function for General Constraint Optimization Problem

In this paper, a Newton algorithm containing a regulated parameter type for sloving general constraint optimization problem is provided. The algorithm possesses two important characters. Firstly, with the help of Lagrange function and F-B function of NCP, it sloves general constraint optimization problem by constructing the linear equations of equating K-T point condition. Moreover,it makes use of the smooth property of F-B function to define a regulate parameter and therefore weakens the K-T point condition. It is proved that the algorithm is global convergence under the appropriate conditions. The numberical results show the algorithm is effective.