优化方法

期末上机大作业

姓 名：李岚松

学 部：电信学部电气工程

学 号

2016 年 11 月 9 日

1°最速下降法

//最速下降法主函数//

function lls=di1titidu(x)=di1titidu(x)

x0=x; eps=1e-4; k=0; g0=g(x0); s0=4; k=0; g0=g(x0); s0=-g0;

while (k>=0)

if norm(g0)

break;

else

lanmed=10;c=0.1;i=0; lanmed=10;c=0.1;i=0;

while i>=0&&i<100 100

x=x0+lanmed*s0;

if f(x)>(f(x0)+c*lanmed*g0'*s0) f(x)>(f(x0)+c*lanmed*g0'*s0)

lanmed=lanmed/2; lanmed=lanmed/2;

i=i+1;

else

break;

end

end

x=x0+lanmed*s0;

x0=x;

g0=g(x);

s0=-g0;

k=k+1;

end

end

lls=x;

sll=f(x);

fprintf('after %d iterations,obtain the optimal solution.iterations,obtain the optimal solution.\n\\nThe optimal

solution is %f.\n\n The optimal "x" is "ans".n The optimal "x" is "ans".\n',k,sll);

//f(x)//

function f=f(x)

x1=[1 0]*x;

x2=[0 1]*x;

f=(1-x1)^2+100*(x2-x1^2)^2;

//梯度函数//

function g=g(x)

x1=[1 0]*x;

x2=[0 1]*x;

g=[-2*(1-x1)-400*x1*(x2-x1^2);

200*(x2-x1^2)];

//运行过程//

>> x=[0;0]

x =

0

0

>> di1titidu(x)

after 4574 iterations,obtain the optimal solution.

The optimal solution is 0.000000.

The optimal "x" is "ans".

ans =

1.0001

1.0002

2 °牛顿法

//牛顿法主函数//

function s=di2tinewton(x)

x0=x; eps=1e-4; k=0;

g0=g(x0); h0=h(x0);s0=-inv(h0)*g0;

while (k>=0&&k<1000)

if norm(g0)

break;

else

x=x0+s0;

x0=x;

g0=g(x);

h0=h(x);

s0=-in