最速下降梯度法Matlab程序.doc

%最速下降梯度法matlab程序% Steepest Descent Method% By Kshitij Deshpandeclcclear allwarning offprompt = Coeficients if X1=,Coefficients of X2=,Coefficeint of X1X2=,Initial Point=;def = 2 1 0,1 -1 0,2,0 0;a=inputdlg(prompt,Data,1,def);a=char(a);m,n=size(a);x1 = eval(a(1,1:n);x2=eval(a(2,1:n);x1x2=eval(a(3,1:n);X1=eval(a(4,1:n);delf1(1) = polyval(polyder(x1),X1(1);delf1(1) = (delf1(1)+(x1x2*X1(2);delf1(2) = polyval(polyder(x2),X1(1);delf1(2) = (delf1(2)+(x1x2*X1(1);s=-delf1;%reportsrep(1,1:2)=s;% x1new(1)=s(1)2;x1new(2)=2*X1(1)*s(1);x1new(3) = X1(1)2; x1new=x1new*x1(1); x1new_(2)=x1(2)*s(1);x1new_(3)=x1(2)*X1(1); x1new = x1new+x1new_; x2new(1)=s(2)2;x2new(2)=2*X1(2)*s(2);x2new(3) = X1(2)2; x2new=x2new*x2(1); x2new_(2)=x2(2)*s(2);x2new_(3)=x2(2)*X1(2); x2new = x2new+x2new_; x1x2new(1)=s(1)*s(2);x1x2new(2)=X1(1)*s(2)+X1(2)*s(1);x1x2new(3)=X1(1)*X1(2); x1x2new=x1x2*x1x2new; df = polyder(x1new+x2new+x1x2new); lambda(1) = roots(df); X1=X1+lambda(1)*s; Xrep(1,1:2)=X1; delf1(1) = polyval(polyder(x1),X1(1); delf1(1) = (delf1(1)+(x1x2*X1(2); delf1(2) = polyval(polyder(x2),X1(2); delf1(2) = (delf1(2)+(x1x2*X1(1);if all(X1)= 0 fprintf(%d %d is the optimum point,X1(1),X1(2);enditrep(1)=1;it=2;while all(delf1)=1 s=-delf1; x1new(1)=s(1)2;x1new(2)=2*X1(1)*s(1);x1new(3) = X1(1)2; x1new=x1new*x1(1); x1new_(2)=x1(2)*s(1);x1new_(3)=x1(2)*X1(1); x1new = x1new+x1new_; x2new(1)=s(2)2;x2new(2)=2*X1(2)*s(2);x2new(3) = X1(2)2; x2new=x2new*x2(1); x2new_(2)=x2(2)*s(2);x2new_(3)=x2(2)*X1(2); x2new = x2new+x2new_; x1x2new(1)=s(1)*s(2);x1x2new(2)=X1(1)*s(2)+X1(2)*s(1);x1x2new(3)=X1(1)*X1(2); x1x2new=x1x2*x1x2new; df = polyder(x1new+x2new+x1x2new); lambda(it) = roots(df); X1=X1+lambda(it)*s; delf1(1) = polyval(polyder(x1),X1(1); delf1(1) = (delf1(1)+(x1x2*X1(2); delf1(2) = polyval(polyder(x2),X1(2); delf1(2) = (delf1(2)+(x1x2*X1(1); itrep(it)=it; srep(it,1:2)=s; Xrep(it,1:2)=X1; it=it+1;endm,n=size(itrep);matrix=itrep srep(1:n,1) srep(1:n,2) Xrep(1:n,1) Xrep(1:n,2);answer = char(num2str(X1);answer = The optimal point is answer ;msgbox(answer,Solution);disp( Press Any key to View Detailed Report.);pauseecho offreport steep;clc -%最速下降法（爬山法）的一个matlab程序function y=steepest(x)%This program uses the steepest descent direction algorithm%to calculate the minimum of the function f(x)=x(1)2+2*x(2)2format longeps=input(please input your accuracy:);%eps is the demmanded accuracy on the norm of %the gradient of the objective functionm=1;%m is the count of the iteration step of the algorithmiterstep(1,:)=x;%iterstep contains the intermediate points of iterationwhile norm(gradobject1(x)eps grad=gradobject1(x); alpha=goldsplictobj(x); x=x-alpha*grad; iterstep(m+1,:)=x; m=m+1;endstep=max(size(iterstep)-1plot(iterstep(:,1),iterstep(:,2);%Draw the search trajectory title(The search trajectory of the Steepest dscent direction algorithm);xlabel(x1-axis);ylabel(x2-axis);text(x(1),x(2),The minimum point found by the algorithm);text(iterstep(1,1),iterstep(1,2),The initial point (2,1);gtext(The number of the total iteration steps of the algorithm is:);gtext(The set accuracy in advance is 1.0*10-10);%The following subfunction is on the objective functionfunction y=object1(v)y=v(1)2+2*v(2)2;%The following subfunction is on the gradient of%the objective functionfunction y=gradobject1(v)y(1)=2*v(1);y(2)=4*v(2);%The following subfunction is on the comming%search function of alphafunction y=substi(alpha,x)y=feval(object1,x-alpha*gradobject1(x);%The following subfunction is on the goldspliction%search of the substi functionfunction y=goldsplictobj(x)a=0;b=10;eps=0.01;y1=a+0.382*(b-a);y2=a+0.618*(b-a);while abs(b-a)eps if substi(y1,x)substi(y2,x) a=y1;