一个新的连续可微的单参数填充函数

New Continuously Differentiable Filled Function with One Parameter

填充函数法是求解非线性全局优化问题的有效方法。针对无约束优化问题,在目标函数及其梯度利普希兹连续的基础上,提出了一个新的连续可微的单参数填充函数,并研究了该填充函数的相关性质。最后,给出了一个填充函数算法,数值实验表明,该填充函数是有效的且算法是可行的。

The filled function method is an effective approach to solve nonlinear global optimization problems. A new filled function with one parameter was proposed when the objective function has some certain conditions for uncon- strained optimization problems, which is continuously differentiable. Then, theoretical properties of the filled function were investigated. At last, the paper gave several numerical experiments. The results show that the filled function is ef- fective and the algorithm is feasible.