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1、%SteepestDescentMethodforMultipleVariableFunctionsclc;closeall;clearall;formatlong;disp('SteepestDescentMethod');disp('=============');%Startingpointsx01=-1;x02=0;%FunctionFinSymbolicFormata='-(3*x1+x2+6*x1*x2-2*(x1^2)+2*(x2^2))';%Insertthedesiredmagnitudeoffinaldirectionv
2、ector(0.0001isfine)eserror=0.0001;%Leavetherestunchanged%=================================symsx1x2%HessianOfFdisp(sprintf('Function=%s',a));A=[diff(diff(a,x1),x1),diff(diff(a,x1),x2);...diff(diff(a,x2),x1),diff(diff(a,x2),x2)];%FirstOrderDerivativeofFB=[diff(a,x1);diff(a,x
3、2)];disp'Hessian......';pretty(simplify(A))disp'Gradient......';pretty(simplify(B))disp('EigenValues');[v,d]=eig(A);disp(d);num_of_iterations=1;symsalphaf=(subs(subs(a,x1,x01),x2,x02));disp(sprintf('f(x0)=%f',f));while(num_of_iterations<7)disp('____________________________
4、_____________');disp(sprintf('Iteration=%d',num_of_iterations));temp=(subs(subs(B,x1,x01),x2,x02));disp(sprintf('GradientofX%d',num_of_iterations-1));disp(temp);temp4=([x01;x02]);disp(sprintf('X%d=',num_of_iterations-1));disp(temp4);temp=temp4-alpha.*(temp);disp(sprintf('X
5、%d-alpha.gradient(X%d)=',num_of_iterations-1,num_of_iterations-1));disp(temp);f_alpha=subs(subs(a,x1,temp(1,1)),x2,temp(2,1));disp(sprintf('f(X%d-alpha.gradient(X%d))=',num_of_iterations-1,num_of_iterations-1));disp(f_alpha);diff_f_alpha=diff(f_alpha,alpha);disp(sprintf('d
6、iff(f(X%d-alpha.gradient(X%d)))/diffalpha=',num_of_iterations-1,num_of_iterations-1));disp(diff_f_alpha);alphaval=solve(diff_f_alpha,'alpha')alphaval2=eval(alphaval)ifalphaval2<0disp'Diverges';break;endnewxkplus1=[x01;x02]-alphaval2.*(subs(subs(B,x1,x01),x2,x02));x01=newxk
7、plus1(1,1);x02=newxkplus1(2,1);disp(sprintf('x%d=',num_of_iterations));disp(newxkplus1)num_of_iterations=num_of_iterations+1;f=(subs(subs(a,x1,x01),x2,x02));disp(sprintf('f(x%d)=%f',num_of_iterations,f));end
