http://www.jasoncantarella.com/downloads/NelderMeadProof.pdf
A simplex method for
- finding a local minimum of a function of several variables
- has been devised by Nelder and Mead. For two variables,
- a simplex is a triangle, and
- the method is a pattern search that compares function values at the three vertices of a triangle.
- The worst vertex, where f (x, y) is largest, is rejected and replaced with a new vertex.
- A new triangle is formed and the search is continued.
- The process generates a sequence of triangles (which might have different shapes), for which
- the function values at the vertices get smaller and smaller.
- The size of the triangles is reduced and the coordinates of the minimum point are found.
The algorithm is stated using the term simplex (a generalized triangle in N dimensions) and will find the minimum of a function of N variables. It is effective and computationally compact.
Logical Decisions for Each Step
A computationally efficient algorithm should perform function evaluations only if needed. In each step, a new vertex is found, which replaces W. As soon as it is found, further investigation is not needed, and the iteration step is completed. Thelogical details for two-dimensional cases are explained in Table 8.5.
总结：如果是只有三个点的话，有点儿像那个二分法。目的：求最小值
，先按照大小排序，从小到大依次记为B,G,W，想找一个点替换掉最大的W。
首先就是把把值最大的那个点对称的映射到其余两个点所在的线的另一边去，得到一个新点记做R，假如这个R的值落在B,G这一头，如果比B的值还小，就取这个R点
否则有理由认为可能沿着这个方向拉伸一下得到更小的值E点，E点的值要是真变小了，就取为E点；
如果对称过去的这个R点的值落在G,W这一头，如果比W小，取为R点
否则就把G,W收缩一下，得到新的三角形。