运筹学的一次作业，用精确直线搜索的梯度法求解非线性规划问题。

ReadMe.md

运行结果

OR_HW1.m

function []=OR_HW1()
x=[0,0];
dfx_val = dfx(x);
normdfx = norm(dfx_val);
k = 0;
f_val = zeros(1000,1);
while normdfx>1e-6
    t = newton(x,-dfx_val);
    x = x-t*dfx_val;
    dfx_val = dfx(x);
    normdfx = norm(dfx_val);
    k = k+1;
    f_val(k) = f(x);
end
format long;
disp('最优解：');x
disp('最优函数值：');f(x)
fprintf('总迭代次数：%d\n',k);
plot((1:k),f_val(1:k));title('函数值与迭代次数关系图');
end

function [val] = f(x)
val=(1-x(1))^2+2*(x(2)-x(1)^2)^2;
end

function [val] = dfx(x)
val(1)=-2*(1-x(1))-8*x(1)*(x(2)-x(1)^2);
val(2)=4*(x(2)-x(1)^2);
end

function [a] = newton(x,p)
syms t;
ff = (1-(x(1)+t*p(1)))^2+2*((x(2)+t*p(2))-(x(1)+t*p(1))^2)^2;
df = diff(ff);
phi = t-df/diff(df);
a=10;nexta=0;
while abs(a-nexta)>1e-4
    a=nexta;
    nexta = double(subs(phi,t,a));
end
end