nelder_mead优化算法

function [xo,fo] = Nelder0(f,abc,fabc,TolX,TolFun,k) %二维空间中的多边形逼近 if nargin < 6 k = 100; end if nargin < 5 TolFun = 1e-8; end if nargin < 4 TolX = 1e-5; end %%%%确定三个顶点a，b，c并且其函数值按从小到大排列 [fabc,I] = sort(fabc); %将二维空间中的多边形三个顶点的函数值按从小到大顺序排列 a = abc(I(1),:); b = abc(I(2),:); c = abc(I(3),:); fa = fabc(1); fb = fabc(2); fc = fabc(3); %%%判断三点或三点函数值的距离是否小于给定阈值.若小于阈值停止循环，得最优解x0=a fba = fb - fa; %a,b点函数值之差 fcb = fc - fb; %b，c点函数值之差 if k <= 0 | abs(fba) + abs(fcb) < TolFun | abs(b - a) + abs(c - b) < TolX xo = a; fo = fa; %小于阈值 else %大于阈值，更新多边形顶点 m = (a + b)/2; e = 3*m - 2*c; %扩展（expansion） fe = feval(f,e); if fe < fb c = e; fc = fe; else r = (m+e)/2; %反射（reflection） fr = feval(f,r); if fr < fc c = r; fc = fr; end if fr >= fb s = (c + m)/2; %内收缩（inside contraction） fs = feval(f,s); if fs < fc c = s; fc = fs; else b = m; c = (a + c)/2; %变小（shrink） fb = feval(f,b); fc = feval(f,c); end end end [xo,fo] = Nelder0(f,[a;b;c],[fa fb fc],TolX,TolFun,k - 1); end