The Nelder-Mead Algorithm in Two Dimensions

最新推荐文章于 2025-06-23 07:30:00 发布

转载最新推荐文章于 2025-06-23 07:30:00 发布 · 302 阅读

algorithm 专栏收录该内容

10 篇文章

订阅专栏

本文介绍了Nelder-Mead算法的一个迭代步骤。首先对顶点进行排序，然后反射最差的点并通过比较成本来确定是否扩展或收缩。该算法适用于不需要导数的优化问题。

http://people.duke.edu/~hpgavin/cee201/Nelder-Mead-2D.pdf

Steps for one iteration of the Nelder-Mead Algorithm

1. Sort the vertices such that f(u) < f(v) < f(w). Point u is the best point, point v is the next-to-worst point, and point w is the worst point.

2. Reflect the worst point, w, through the centroid of the remaining points (u and v) to obtain the reflected point, r, and evaluate f(r).

If the cost at the reflected point, f(r), is between the best and next-to-worst cost (f(u) <f(r) < f(v)) then replace the worst point, w, with the reflected point, r, and go to step 5

3. If the cost at the reflected point, f(r), is better than f(u) (f(r) < f(u)) then extend the reflected point, r, further past the average of u and v, to point e, and evaluate f(e).

(a) If the cost at the extended point, f(e), is better than the reflected point cost, f(r), then replace the worst point, w, with the extended point, e, and go to step 5.

(b) Otherwise replace the worst point, w with the reflected point, r, and go to step 5.

4. If the inequalities of steps 2 and 3 are not satisfied, then it is certain that the reflected point, r, is worse than the next-to-worst point, v, (f(r) > f(v)) and, a smaller value of f might be found between points w and r. So try to contract the worst point, w, to a point c between w and r, and evaluate f(w). The best distance along the line from w to r can be hard to

determine, and, in general, it is not worth trying too hard to find this minimum. Typicalvalues of c are one-quarter and three-quarters of the way from w to r. These are called insideand outside contraction points, ci and co.