非线性优化的直接搜索算法及收敛性证明

A Direct Searching Method for Nonlinear Optimizing Problems and Its Convergence Proof

研究非线性函数的优化问题.在很多实际问题中,会遇到求连续函数的极值问题.如果目标函数不存在导数,或者导数很难求得,一些高精度的极值计算方法就不能使用.针对这一问题给出相应的直接搜索算法,证明了算法的收敛性,并给出一些算例.最后将这一算法运用于分形粗糙面的反演问题中,得到了很好的反演效果.

The optimizing problems of nonlinear functions are discussed. In a lot of practical problems,one often encounters the extreme problem of continuous functions. If the derivative of the objective function does not exist or is difficult to be calculated,some high precision optimal methods cannot be used. A direct searching method without computing the derivative functions is given. The convergence for this method is proved and applied to solve inverse problem of fractal rough surface.