2024年3月21日发(作者：查曼岚)
%最速下降梯度法matlab程序
% Steepest Descent Method
% By Kshitij Deshpande
clc
clear all
warning off
prompt = {'Coeficients if X1=','Coefficients of X2=','Coefficeint
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));
of
delf1(1) = (delf1(1))+(x1x2*X1(2));
delf1(2) = polyval(polyder(x2),X1(1));
delf1(2) = (delf1(2))+(x1x2*X1(1));
s=-delf1;
%%%%%%%%%%
%report
srep(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));
end
itrep(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;
end
[m,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 ');
pause
echo off
report 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)^2
format long
eps=input('please input your accuracy:');
%eps is the demmanded accuracy on the norm of
%the gradient of the objective function
m=1;
%m is the count of the iteration step of the algorithm
iterstep(1,:)=x;
%iterstep contains the intermediate points of iteration
while norm(gradobject1(x))>eps
grad=gradobject1(x);
alpha=goldsplictobj(x);
x=x-alpha*grad;
iterstep(m+1,:)=x;
m=m+1;
end
step=max(size(iterstep))-1
plot(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 function
function y=object1(v)
y=v(1)^2+2*v(2)^2;
%The following subfunction is on the gradient of
%the objective function
function y=gradobject1(v)
y(1)=2*v(1);
y(2)=4*v(2);
%The following subfunction is on the comming
%search function of alpha
function y=substi(alpha,x)
y=feval('object1',x-alpha*gradobject1(x));
%The following subfunction is on the goldspliction
%search of the substi function
function 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;
b=b;
y1=a+0.382*(b-a);
y2=a+0.618*(b-a);
elseif substi(y2,x)>substi(y1,x)
a=a;
b=y2;
y1=a+0.382*(b-a);
y2=a+0.618*(b-a);
else
a=y1;
b=y2;
y1=a+0.382*(b-a);
y2=a+0.618*(b-a);
end
end
y=(y1+y2)/2;
2024年3月21日发(作者：查曼岚)
%最速下降梯度法matlab程序
% Steepest Descent Method
% By Kshitij Deshpande
clc
clear all
warning off
prompt = {'Coeficients if X1=','Coefficients of X2=','Coefficeint
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));
of
delf1(1) = (delf1(1))+(x1x2*X1(2));
delf1(2) = polyval(polyder(x2),X1(1));
delf1(2) = (delf1(2))+(x1x2*X1(1));
s=-delf1;
%%%%%%%%%%
%report
srep(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));
end
itrep(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;
end
[m,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 ');
pause
echo off
report 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)^2
format long
eps=input('please input your accuracy:');
%eps is the demmanded accuracy on the norm of
%the gradient of the objective function
m=1;
%m is the count of the iteration step of the algorithm
iterstep(1,:)=x;
%iterstep contains the intermediate points of iteration
while norm(gradobject1(x))>eps
grad=gradobject1(x);
alpha=goldsplictobj(x);
x=x-alpha*grad;
iterstep(m+1,:)=x;
m=m+1;
end
step=max(size(iterstep))-1
plot(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 function
function y=object1(v)
y=v(1)^2+2*v(2)^2;
%The following subfunction is on the gradient of
%the objective function
function y=gradobject1(v)
y(1)=2*v(1);
y(2)=4*v(2);
%The following subfunction is on the comming
%search function of alpha
function y=substi(alpha,x)
y=feval('object1',x-alpha*gradobject1(x));
%The following subfunction is on the goldspliction
%search of the substi function
function 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;
b=b;
y1=a+0.382*(b-a);
y2=a+0.618*(b-a);
elseif substi(y2,x)>substi(y1,x)
a=a;
b=y2;
y1=a+0.382*(b-a);
y2=a+0.618*(b-a);
else
a=y1;
b=y2;
y1=a+0.382*(b-a);
y2=a+0.618*(b-a);
end
end
y=(y1+y2)/2;