最优化方法实验报告2

最优化方法实验报告

实验一：用进退法求函数 的一个形如 的初始区间。

程序如下：

function [minx,maxx] = minJT(f,x0,h0,eps)

format long;

if nargin == 3

eps = 1.0e-6;

end

x1 = x0;

k = 0;

()22+-=x x x f []b ,0

h = h0;

while 1

x4 = x1 + h;

k = k+1;

f4 = subs(f, findsym(f),x4); f1 = subs(f, findsym(f),x1); if f4 < f1

x2 = x1;

x1 = x4;

f2 = f1;

f1 = f4;

h = 2*h;

else

if k==1

h = -h;

x2 = x4;

f2 = f4;

else

x3 = x2;

x2 = x1;

x1 = x4;

break;

end

end

end

minx = min(x1,x3);

maxx = x1+x3 - minx;

format short;

窗口中输入：

syms x;

f= x*x-x+2;

[minx,maxx] = minJT(f,0,0.01,eps) minx =

0.3100

maxx =

1.2700

实验二：用黄金分割法求函数在区间[]3,1-上的极小

()2

2+

-

=x

x

x

f

点。

程序为：

function [x,minf] = minHJ(f,a,b,eps) format long;

if nargin == 3

eps = 1.0e-6;

end

l = a + 0.382*(b-a);

u = a + 0.618*(b-a);

k=1;

tol = b-a;

while tol>eps && k<100000

fl = subs(f , findsym(f), l);

fu = subs(f , findsym(f), u);

if fl > fu

a = l;

l = u;

u = a + 0.618*(b - a);

else

b = u;

u = l;

l = a + 0.382*(b-a);

end

k = k+1;

tol = abs(b - a);

end

if k == 100000

disp('找不到最小值！');

x = NaN;

minf = NaN;

return;

end

x = (a+b)/2;

minf = subs(f, findsym(f),x);

format short;

在窗口中输入：

>> syms x;

>> f=x^2+x-2;

>> [x,fx]=minHJ(f,-1,3)

x =

-0.5115

fx =

-2.249

实验三：用wolf 准则求函数()()()212

2121100x x x x f -+-= 在点()T k x 0,0=沿方向()T

k p 0,1=的近似步长。 程序为：调用到的Usearch1程序:

function result=Usearch1(f,x1,x2,df,x0,p)

mu=0.001;sgma=0.99;a=0;b=inf;arf=1;m_count=0;s_count=0;

pk=p;

x3=x0;

x4=x3+arf*pk;m_count=m_count+2;s_count=s_count+2;

f1=subs(f,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+4;s_count=s_count+3; f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+4;s_count=s_count+3; gk1=subs(df,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+7;s_count=s_count+4; gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+7;s_count=s_count+4; while (f1-f2<=-mu*arf*gk1'*pk)

b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});

m_count=m_count+19;s_count=s_count+12;

end;

m_count=m_count+5;s_count=s_count+2;

while (1>0)

if(gk2'*pk

a=arf;a=min(2*arf,(a+b)/2);x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk 2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});

m_count=m_count+21;s_count=s_count+12;

while (f1-f2<=-mu*arf*gk1'*pk)

b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});

m_count=m_count+19;s_count=s_count+12;

end;

m_count=m_count+5;s_count=s_count+2;

else

break;