matlab鲍威尔法（Powell）

%改进鲍威尔法
clc
clear all

syms x1 x2 a1 a2 a3 b1 b2 b3
f = x1*x1+2*x2*x2-4*x1-2*x1*x2;
X=[x1;x2];
X0=[1 1]'; %给定初始点
Theta_error=0.001;
e1=[1 0]';
e2=[0 1]';

FX0=subs(f,X,X0);

n=2;
k=0;
k1=0;
k2=0;
d1=e1;%初始搜搜方向
d2=e2;
i=1;

%求a1，a2，X1,X2
Da1=[];
Da2=[];
Da3=[];
DX0=[];
DX00=[];
DXX0=[];
DXXX0=[];
DX1=[];
DX11=[];
DX2=[];
DX22=[];
DX3=[];
DX33=[];
DF=[];

Xh1 = X0+a1.*d1;
FXh1 = subs(f,X,Xh1);
dFXh1 = gradient(FXh1,a1);
a1 = solve(dFXh1);
f = x1*x1+2*x2*x2-4*x1-2*x1*x2;

X1 = X0+a1*e1;
FX1 = subs(f,X,X1);

Xh0 = X1+a2.*d2;
FXh2 = subs(f,X,Xh0);
dFXh0 = gradient(FXh2,a2);
a2 = solve(dFXh0);
X2 = X1+a2*e2;
FX2 = subs(f,X,X2);

deta1 = FX0-FX1;
deta2 = FX1-FX2;
m = [deta1,deta2];
M=sort(m); %将deta从小到大排序，然后最后一位就是最大值
deta_Max=M(2);

%k=1
d3=X2-X0;
X3=2*X2-X0;
FX3 = subs(f,X,X3);

if FX3 < FX0 && (FX0-2*FX2+FX3)*(FX0-FX2-deta_Max)^2 < 0.5*deta_Max*(FX0-FX3)^2
XX0=X2+a3.*d3;
h0=X2+a3.*d3;
Fh0 = subs(f,X,h0);
dFh0 = gradient(Fh0,a3);
a3 = solve(dFh0);
XX0=X2+a3.*d3;
d1=d2;
d2=d3;
else
d1=d1;
d2=d2;
if FX2<FX3
XX0=X2;
else
XX0=X3;
end
end
while norm(XX0-X0) >= Theta_error

k=k+1;
X0=XX0; DX0(k)=X0(1);DX00(k)=X0(2);
%求a1，a2，X1,X2
a1=b1;
Xh1 = XX0+a1.*d1;
FXh1 = subs(f,X,Xh1);
dFXh1 = gradient(FXh1,b1);
a1 = solve(dFXh1); Da1(k)=a1;
f = x1*x1+2*x2*x2-4*x1-2*x1*x2;


X1 = XX0+a1.*d1; DX1(k)=X1(1);DX11(k)=X1(2);
FX1 = subs(f,X,X1);

a2=b2;
Xh0 = X1+a2.*d2;
FXh2 = subs(f,X,Xh0);
dFXh0 = gradient(FXh2,b2);
a2 = solve(dFXh0); Da2(k)=a2;
X2 = X1+a2.*d2; DX2(k)=X2(1);DX22(k)=X2(2);
FX2 = subs(f,X,X2);

FX0 = subs(f,X,XX0);

deta1 = FX0-FX1;
deta2 = FX1-FX2;
m = [deta1,deta2];
M=sort(m); %将deta从小到大排序，然后最后一位就是最大值
deta_Max=M(2);


if FX3 < FX0 && (FX0-2*FX2+FX3)*(FX0-FX2-deta_Max)^2 < 0.5*deta_Max*(FX0-FX3)^2
%走该条通道看k1++
k1=k1+1;
a3=b3; Da3(k)=a3;
XX0=X2+a3*d3;
h0=X2+a3*d3;
Fh0 = subs(f,X,h0);
dFh0 = gradient(Fh0,a3);
a3 = solve(dFh0); Da3(k)=a3;
XX0=X2+a3*d3; DXX0(k)=XX0(1);DXXX0(k)=XX0(2);DF(k)=subs(f,X,XX0);
d1=d2;
d2=d3;
else
%走该条通道看k2++
k2=k2+1;
if FX2<FX3
XX0=X2; DXX0(k)=XX0(1);DXXX0(k)=XX0(2);DF(k)=subs(f,X,XX0);
else
XX0=X3; DXX0(k)=XX0(1); DXXX0(k)=XX0(2);DF(k)=subs(f,X,XX0);
end
end

%axis([0 10 0 10]);
plot(XX0(1),XX0(2),'rp')
%plot(X0(1),X0(2),'b*')
line([X0(1) X1(1)],[X0(2) X1(2)]);
line([X0(1) X2(1)],[X0(2) X2(2)]);
line([X1(1) X2(1)],[X1(2) X2(2)]);
line([X0(1) XX0(1)],[X0(2) XX0(2)]);
hold on
end
grid on
axis([3 5 0 4])
ezplot('-8 =x1*x1+2*x2*x2-4*x1-2*x1*x2')
hold on
ezplot('-7.998 =x1*x1+2*x2*x2-4*x1-2*x1*x2')
hold on
ezplot('0 =x1*x1+2*x2*x2-4*x1-2*x1*x2')
hold on

X_output=XX0;
FX_output= subs(f,X,X_output);

%double(X_output);double(FX_output);
X_output,FX_output

matlab鲍威尔法（Powell）相关推荐

基于matlab GUI Powell+蚁群算法图像配准
基于matlab GUI Powell+蚁群算法图像配准一.简介 1 蚁群算法(ant colony algorithm,ACA)起源和发展历程 Marco Dorigo等人在研究新型算法的过程中, ...
鲍威尔方法c语言程序,鲍威尔法编程-powell法编程-c语言编程-c++6.0.doc
鲍威尔法编程-powell法编程-c语言编程-c++6.0.doc include stdio.hdefine N 2float gsfloat zNfloat f;f10*z0z1-5*z0z1-5 ...
newuoa matlab包,PDFO首页、文档和下载 - Powell 无导数优化求解器
PDFO(Powell's Derivative-Free Optimization solvers,Powell 无导数优化求解器)为 Michael J. D. Powell 的无导数优化求解器提 ...
鲍威尔法源程序码matlab,鲍威尔算法matlab程序f.doc
鲍威尔算法matlab程序f.doc functionf=fun(x)f=10*(x(1)+x(2)-5)^2+(x(1)-x(2))^2;functionf=fx(x0,alpha,s)x1=x0+ ...
matlab使用sym类型，subs和diff函数，进行模式搜索法和改进的powell法求解函数
如果想以分数输出结果,可以用 format rat f函数使用以前的稍加改造 function y=f(x) if(length(x)==1)global xk;global pk;x=xk+x* ...
鲍威尔c 语言程序,鲍威尔法编程-powell法编程 c语言编程 c++6.0
fafu js 优化 #include #define N 2 float gs(float z[N]) { float f; //f=10*(z[0]+z[1]-5)*(z[0]+z[1]-5)+( ...
matlab 求极小值一维优化,MATLABoptimization
MATLABoptimization 所属分类:matlab例程开发工具:matlab 文件大小:38KB 下载次数:4146 上传日期:2010-01-06 22:50:12 上传者:百位过 ...
一维搜索-黄金分割法matlab实现
一维搜索-黄金分割法matlab实现前言 1.黄金分割法 1.1 黄金分割法的定义 1.2 黄金分割法的搜索过程 2.黄金分割matlab实现 2.1 求f(x)=x^2-7*x+10的极值 2.2 ...
混合罚函数法matlab报错,罚函数法MATLAB程序
一.进退法.0.618法.Powell法.罚函数法的Matlab程序设计罚函数法(通用) function y=ff(x,k) y=-17.86*0.42*x(1)/(0.8+0.42*x(1))* ...
matlabff2函数_罚函数法MATLAB程序.doc
罚函数法MATLAB程序一.进退法.0.618法.Powell法.罚函数法的Matlab程序设计罚函数法(通用)function y ff x,k y -17.86*0.42*x 1 / 0.8+0 ...

matlab鲍威尔法（Powell）

matlab鲍威尔法（Powell）相关推荐

最新文章

热门文章