bs.m

function []=bs()
x=[0,0];
dfx_val = dfx(x);
normdfx = norm(dfx_val);
k = 0;
f_val = zeros(1000,1);
dfx_val_pre = [1,1];
p_pre = [0,0];
while normdfx>1e-10
    if mod(k,2) == 0
        p = -dfx_val;
    else
        p = -dfx_val + dfx_val*(dfx_val-dfx_val_pre)'/...
            (p_pre*(dfx_val-dfx_val_pre)')*p_pre;
    end
    t = newton(x,p,1e-10);
    p_pre = p;
    dfx_val_pre = dfx_val;
    x = x+t*p;
    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

fr.m

function []=fr()
x=[0,0];
dfx_val = dfx(x);
normdfx = norm(dfx_val);
k = 0;
f_val = zeros(1000,1);
normdfx_pre = normdfx;
p_pre = [0,0];
while normdfx>1e-10
    if mod(k,2) == 0
        p = -dfx_val;
    else
        p = -dfx_val + normdfx^2/normdfx_pre^2*p_pre;
    end
    t = goldstein(x,p,[0.3,0.7]);
    p_pre = p;
    normdfx_pre = normdfx;
    x = x+t*p;
    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

goldstein.m

function [ a ] = goldstein( x,p,m )
syms t;
alpha = 1.5;
ff = (1-(x(1)+t*p(1)))^2+2*((x(2)+t*p(2))-(x(1)+t*p(1))^2)^2;
ff0 = double(subs(ff,t,0));
df = diff(ff);
df0 = double(subs(df,t,0));
a = 0; b = Inf; k = 0; q = 1;
while (1)
    phit = double(subs(ff,t,q));
    if phit<= ff0+m(1)*q*df0
        if phit>= ff0+m(2)*q*df0
            a = q;
            break;
        else
            a = q;
        end
    else
        b = q;
    end
    if b == Inf
        q = alpha*q;
    else
        q = (a+b)/2;
    end
    k = k + 1;
end
end

gradient.m

function []=gradient()
x=[0,0];
dfx_val = dfx(x);
normdfx = norm(dfx_val);
k = 0;
f_val = zeros(1000,1);
while normdfx>1e-10
    t = newton(x,-dfx_val,1e-10);
    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

newton.m

function [a] = newton(x,p,eps)
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)>eps
    a=nexta;
    nexta = double(subs(phi,t,a));
end
end

pr.m

function []=pr()
x=[0,0];
dfx_val = dfx(x);
normdfx = norm(dfx_val);
k = 0;
f_val = zeros(1000,1);
dfx_val_pre = [0,0];
normdfx_pre = normdfx;
p_pre = [0,0];
while normdfx>1e-10
    if mod(k,2) == 0
        p = -dfx_val;
    else
        p = -dfx_val + dfx_val*(dfx_val-dfx_val_pre)'/normdfx_pre^2*p_pre;
    end
    t = newton(x,p,1e-10);
    p_pre = p;
    normdfx_pre = normdfx;
    dfx_val_pre = dfx_val;
    x = x+t*p;
    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