How find the value of V=V0,V1,...,Vn.

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SHAHID
SHAHID 2024-6-12
评论： SHAHID 2024-6-13
close all
clc
function V=L(Z,r,m,n,u)
Z=2;
n=5;
m=5;
r=0.2;
h=1/m;
% First for loop
for i=0:n
xi=i/n;
% if condition for xi-r
if xi-r< r
lflag=1;
else
j=find(xi-r<Y,1)-1;
alpha=(xi-r-Y(j))/h;
V=Y(j)+alpha*(Y(j+1)-Y(j));
end
% if condition for xi+r
if xi+r>1-r
uflag=1;
else
k=find(xi+r>Y)+1;
alpha=(xi+r-y(k-1))/h;
W=y(k-1)+alpha(Y(k)-Y(k-1));
end
% lflag and uflag conditions for trapz
if lflag == 1 && uflag == 1
w(i+1) = h * trapz(u);
elseif lflag == 1
w(i+1) = h * trapz(u(1:k-1)) + (xi+r-Y(k-1))/2 * (u(k-1) + W);
elseif uflag == 1
w(i+1) = Y(j+1) - (xi-r)/2 * (V + u(j+1)) + h * trapz(u(j+1:end));
else
w(i+1) = Y(j+1) - (xi-r)/2 * (V + u(j+1)) + h * trapz(u(j+1:k-1)) + (xi+r-Y(k-1))/2 * (u(k-1) + W);
end
end
% Another for loop
n=5;
h=1/n;
for i=0:n
V(i+1)=Z/2*h*trapz(w(1:i+1));
end
end
disp(V);
u=u0,u1,...,un are unknown vectors between [0,1]. Y(j)=r+j/m(1-2r), y=y0,y1,...,ym.

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回答（1 个）

Nipun
Nipun 2024-6-13
Hi Shahid,
I understand that you want to minimize the given expression subject to the constraints. Based on the shared information, I recommend using non-linear minimization option built-in in MATLAB to achieve the desired results.
Here is the link to documentation for "fmincon" function in MATLAB used to find minimum of constrained nonlinear multivariable function: https://www.mathworks.com/help/optim/ug/fmincon.html
Hope this helps.
Regards,
Nipun
  1 个评论
SHAHID
SHAHID 2024-6-13
Dear Sir, can you give suggestion for writing code with fmincon because its new for me. I will wait your response. Thanks

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