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

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.

[Aquatris]

What exactly is the question?

[SHAHID]

I want to minimize this function.

Answer 1

[Nipun]

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

[SHAHID]

Dear Sir, can you give suggestion for writing code with fmincon because its new for me. I will wait your response. Thanks