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matlab腳本文件,通用代碼,求現(xiàn)代設(shè)計(jì)方法中二維無約束優(yōu)化問題的最優(yōu)解

資源截圖

代碼片段和文件信息


%%????
X_1_0=[0;0];
precise=0.0001;
S_1_1=[1;0];
S_1_2=[0;1];
k=1
syms?alpha1?alpha2?alpha3??x1?x2?X_1_1?X_1_2;
X=[x1;x2];
%?fx=2*x1^2+x2^2-x1*x2;
%?fx=x1^2+2*x2^2-4*x1-2*x1*x2;
fx=60-10*x1-4*x2+x1^2+x2^2-x1*x2;
while?1

????%求解k次迭代第二個(gè)點(diǎn)的函數(shù)值
????F_1_0=subs(fxX?X_1_0)
%?????disp(F_1_0)
????
????%求解k次迭代第二個(gè)點(diǎn)的函數(shù)值
????X_1_1=X_1_0+alpha1*S_1_1;
????F1=subs(fxX?X_1_1);
????f1=diff(F1);
????alpha1N=solve(f1alpha1);
????X_1_1=X_1_0+alpha1N*S_1_1;
????F_1_1=subs(fxX?X_1_1)
%?????disp(F_1_1)
????
????%求解k次迭代第三個(gè)點(diǎn)的函數(shù)值
????X_1_2=X_1_1+alpha2*S_1_2;
????F2=subs(fxX?X_1_2);
????f2=diff(F2);
????alpha2N=solve(f2alpha2);
????X_1_2=X_1_1+alpha2N*S_1_2;
????F_1_2=subs(fxX?X_1_2)
%?????disp(F_1_2)
????
????%計(jì)算共軛方向
????S_1=X_1_2-X_1_0
????X_1_3=2*X_1_2-X_1_0;
????F_1_3=subs(fxX?X_1_3)
%?????disp(F_1_3)
????
????data_1_1=F_1_0-F_1_1;
????data_1_2=F_1_1-F_1_2;
????if(data_1_1>data_1_2)
????????S_m_k=S_1_1;
????????data_m_k=data_1_1;
????????f_1=(F_1_0-2*F_1_2+F_1_3)*(F_1_0-F_1_2-data_m_k)^2;
????????f_2=(0.5*data_m_k*(F_1_0-F_1_3)^2);
????????if((F_1_3????????????X_1=X_1_2+alpha3*S_1;
????????????F3=subs(fxX?X_1);
????????????f3=diff(F3);
????????????alpha3N=solve(f3alpha3)
????????????X_1=X_1_2+alpha3N*S_1
????????????X_2_0=X_1;
????????????S_1_1=S_1_2
????????????S_1_2=S_1
????????????if?norm(X_2_0-X_1_0)<=precise
????????????????break;
????????????else
????????????????X_1_0=X_1;
????????????????X_star=X_2_0;
????????????????X_star=vpa(X_star)
????????????????f_star=subs(fxX?X_star);
????????????????f_star=vpa(f_star)
????????????????fprintf(‘最優(yōu)解%f‘?X_star)
????????????????k=k+1
????????????end
????????????
????????else
????????????if?F_1_3>F_1_2
???????????????X_2_0=X_1_2;
???????????????if?sqrt((X_2_0(11)-X_1_0(11)).^2+(X_2_0(21)-X_1_0(21)).^2)<=precise
???????????????????break;
???????????????else
???????????????????X_1_0=X_2_0;
???????????????????X_star=X_2_0;
???????????????????X_star=vpa(X_star)
???????????????????f_star=subs(fxX?X_star);
???????????????????f_star

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