求全局最优化问题的单参数替代函数法及其收敛性分析

The Method of Filled Functions with Single Parameter for Global Optimization and its Convergence

本文针对Renpu Ge所提出的双参数替代函数法求解全局最优化问题时不易在计算机上实现的缺陷,构造一类新的单参数替代函数,讨论了它的性质;并对光滑目标函数,给出了如何用二次共轭函数构造单参数替代函数的途径;最后给出了利用这类新的替代函数求全局最优化问题的算法,并证明了其收敛性。

In this paper, a parameter has been eliminated successfully in the new filled functions according to Renpu Ge et al~[1-3] the properties of the new filled functions have been discussed, and the objective function f(x) has been replaced by its double conjugate function f (x) in the new filled functions. Finally, we set up the new method of filled function for global optimization and prove that the method is convergence under some conditions.