变尺度DFP算法MATLAB实例.doc

clear all;close all;clc;syms x1 x2 t;f=4*(x1-5)2+(x2-6)2;f_grad=diff(f,x1);diff(f,x2);X0=8;9;n=10;epsonal=0.01;fx=inline(f);fx_grad=inline(f_grad);X=X0;Xk=X0;while 1 fx0=fx(X0(1),X0(2); fx0_grad=fx_grad(X0(1),X0(2); Hk=eye(2); Pk=-fx0_grad; k=0; while 1 param=Xk+t*Pk; fx1=fx(param(1),param(2); tk,y=equation_extremum(fx1,t,-1,5,epsonal); Xk=Xk+tk*Pk; fx0_k=fx(Xk(1),Xk(2); fx0_grad_k=fx_grad(Xk(1),Xk(2); if fx0_grad_k.*fx0_grad_k=epsonal fx0_grad=fx0_grad_k; break; end if k=n; X=Xk; fx0=fx0_k; fx0_grad=fx0_grad_k; break; end Sk=Xk-X; Yk=fx0_grad_k-fx0_grad; Hk=Hk+Sk*Sk./(Sk.*Yk)-Hk*Yk*Yk.*Hk/(Yk.*Hk*Yk); Pk=-Hk*fx0_grad_k; k=k+1; end if fx0_grad.*fx0_grad=epsonal display(Xk); display(fx0_k); break; endend运行结果：Xk = 5.0000 6.0000fx0_k = 3.2815e-10