matlab 加步探索法确定一维最优化问题(给个源程序)

syms xf=x^3-2*x+1x0=0h=1a=2b=1x1=x0+hfx0=subs(f,x,x0)fx1=subs(f,x,x1)if fx1<fx0 %方向对了，继续山者巧加x2=x1+a^b*h fx2=subs(f,x,x2) while(fx2<fx1)b=b+1 x0=x1 x1=x2 fx0=fx1 fx1=fx2 x2=x1+a^b*h fx2=subs(f,x,x2) endx3=1/2*(x2+x1) fx3=subs(f,x,x3) if fx3<fx1s=[x1,x2] elses=[x0,x3] endelse %方向反了x1=x0-h fx1=subs(f,x,x1) x2=x1-a^b*h fx2=subs(f,x,x2) while(fx2<fx1)b=b+1 x0=x1 x1=x2 fx0=fx1 fx1=fx2 x2=x1-a^b*h fx2=subs(f,x,x2) endx3=1/逗键2*(x1+x2) fx3=subs(f,x,x3) if fx3<fx1s=[x2,x1] elses=[x3,x0] endenddisp('结果区间为嫌闹:')sdisp('搜索次数为:')b

最数下降法解无约束优化的高弊局程序

先建立一维搜索的m文件：minWP.m如下

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [x,minf]=minWP(f,XMAX,c1,c2,alpha,tol)

%一维搜索的Wolfe-Powell法

%作者:龚纯 王正林<<精通 Matlab 最优化计算>>

%f:目标函数

%XMAX:搜索最大值

%c1:可接受系数1

%c2:可接受系数2

%alpha:增大步长倍数

%tol:精度

%x:极小值点

%minf:极小值点处的函数值

format long

if nargin==5

tol=1.0e-6

end

if ~(c1>0)||~(c1<c2)||~(c2<1)||~(XMAX>卜烂0)||~(alpha>1)

error('参数不对')

end

var=findsym(f)

df=diff(f)

f0=subs(f,var,0)

df0=subs(df,var,0)

a=0

b=XMAX

if b<inf

t=(a+b)/2

else

t=10

end

while 1

ft=subs(f,var,t)

fu=f0+c1*t*df0

if ft<=fu

dft=subs(df,var,t)

dfl=c2*t*df0

if dft>dfl

x=t

break

else

a=t

if b==inf

t=t*alpha

else

t=(a+b)/2

end

continue

end

else

b=t

t=(a+b)/2

continue

end

end

minf=subs(f,var,t)

format short

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

然后建立最速下降法的m文件如下：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%minFD.m

function [x,minf]=minFD(f,x0,var,tol)

%最速下降法

%作者：龚纯 王正林《精通Matlab最优化计算》

%目标函数：f

%初始点：x0

%自变量向量：var

%精度：tol

%所求的驻点戚让：x

%驻点处的函数值

format long

if nargin==3

tol=1.0e-6

end

gradf=jacobian(f,var) %f的梯度

wucha=1

syms lamda

while wucha>tol

d=-subs(gradf,var,x0)

wucha=norm(d)

y=x0+lamda*d

yf=subs(f,var,y)

%l=minHJ(yf,0,100)

l=minWP(yf,10,0.2,0.6,2)

x1=x0+l*d

x0=x1

end

x=x1

minf=subs(f,var,x)

format short

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

保存后就可调用了：

>>clear

>>syms x1 x2

>>f=1.5*x1^2+0.5*x2^2-x1*x2-2*x1

f =

3/2*x1^2+1/2*x2^2-x1*x2-2*x1

>>[x,mf]=minFD(f,[-2 4],[x1,x2])

x =

1.00001.0000

mf =

-1.0000

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