Nelder–Mead method

纯属个人见解.

Nelder–Mead method 是一种求解优化问题的方法.不同于"单纯形"方法(Not to be confused with Dantzig's simplex algorithm for the problem of linear optimization).

如果被优化问题中有n个变量,那么需要构造(n+1)个n维的点,这些点的组合称之为"单纯形",所谓单纯形是指: Examples of simplices include a line segment on a line, a triangle on a plane, a tetrahedron in three-dimensional space and so forth.在NM方法中,"单纯形的选择还是停重要的,但是我没有想明白该用什么规则来定这些顶点的值.

NM方法通过不断改变单纯形顶点的值,使得单纯形不断缩小到最优解的周围,直到满足条件退出.

改变单纯形顶点的方法为:(参考自:https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method)

算法可参考资料:

1. matlab 中已经有了NM算法的库函数,可以直接调用.https://blog.youkuaiyun.com/wu_wenhuan/article/details/52786681
2. https://blog.youkuaiyun.com/taojiea1014/article/details/80616580