实用最优化方法Matlab程序设计.docxVIP

实用最优化方法 Matlab 程序设计 程序如下： function lambda = nonexact(x0,s0) g0 = grad(x0); f0=f(x0); a=0; c1=0.1; c2=0.5; lambdak=1; sk=s0; d=-c1*lambdak*g0*sk; xk=x0 + lambdak*sk; f1=f(xk); e=f0-f1; while de lambdak=(lambdak+a)/2; xk=x0 + lambdak*sk; fk=f(xk); e=f0-fk; d=-c1*lambdak*g0*sk; end lambdak function g=grad(x) g=zeros(2,1); g(1)=-4*x(1)*(x(2)-x(1)^2)-2*(1-x(1)); g(2)=2*(x(2)-x(1)^2); function fa=f(x) fa=(x(2)-x(1)^2)^2+(1-x(1))^2; 在命令窗口中输入 x0=[0;1]; s0=[-1;1];nonexact(x0,s0) 输出结果为： 程序如下： function x_star = cong(x0,eps) g0 = grad(x0); res0 = norm(g0); resk=res0; k = 0; xk =x0; while reskeps k=k+1; if k==1 sk=-grad(xk); else end  sk=-grad(xk)+resk^2/res0^2*s0; lambdak=step(xk,sk); x0=xk; xk=x0 + lambdak*sk; res0=resk; resk=norm(grad(xk)); s0=sk; fprintf(------the%d-th iteration, the residual is %f, the lambdak is %f\n\n, k ,resk,lambdak); end x_star=xk; disp(the optimal solution is); x_star %sub functions function g=grad(x) g=zeros(4,1); g(1)=2*x(1)-2*x(2)+2; g(2)=4*x(2)-2*x(1)-x(3)+3; g(3)=2*x(3)-x(2)-1; g(4)=2*x(4); function lambda=step(x,s) a=2*x(1)*s(1)-2*x(2)*s(1)-2*x(1)*s(2)+4*x(2)*s(2)+2*s(3)*x(3)+2*x(4)*s(4)-s(2)*x (3)-s(3)*x(2)+2*s(1)+3*s(2)-s(3); b=2*s(1)^2+4*s(2)^2-4*s(1)*s(2)+2*s(3)^2+2*s(4)^2-2*s(2)*s(3); lambda=-a/b; 在命令窗口中输入 x0=[0;0;0;0];eps=1e-6;cong(x0,eps) 输出结果为 - 当Hk = I2 时 程序如下： function x_star = dfph(x0,eps) g0 = grad(x0); res0 = norm(g0); res=res0; k = 0; xk =x0; while reseps k=k+1; H=eye(length(x0)); sk=-H*grad(xk); lambdak = nonexact(xk,sk); x0=xk; xk=x0 + lambdak*sk; res=norm(grad(xk)); fprintf(------the%d-th iteration, the residual is %f, the lambdak is %f\n\n, k ,res,lambdak); end x_star=xk; disp(the optimal solution is); x_star function lambda = nonexact(x0,s0) g0 = grad(x0); f0=f(x0); a=0; c1=0.1; c2=0.5; lambdak=1; d=-c1*lambdak*g0*s0; xk=x0 + lambdak*s0; f1=f(xk); e=f0-f1; while de lambdak=(lambdak+a)/2; xk=x0 + lambdak*s0; fk=f(xk); e=f0-fk; d=-c1*lambdak*g0*s0; end lambda=lambdak; function g=grad(x) g=zeros(2,1); g(1