How to create an objective function c(t) to use fminserch , struggle with the summatoin , i used the following code for the optimization but it doesn't seem to work

function i= cout(cc,cp,crg,alpha,delta,eta,rho,beta,K,T )
 cc=15000;
 cp=10000;
 crg=200000;
 rho=0.5;
 eta=56.9;
 beta=2.6;
 alpha=1.63;
 delta=0.015;
 s=0;
 T=1:1:600;
 K=20;
 ct=[];Y=[];X=[];
 for K=20 
 s=s+((((K-((K-1).*rho))/eta).^beta-(((K-1)-(K-1).*rho)/eta).^beta)-((((K-1)/eta).^beta).*(beta*delta))).*alpha
 ct=[ct;((crg+cp*(K-1))/(K))*(T.^(-1))+((cc*s)*(T.^(beta-1)))/(K)]
 X=[X,min(ct)];
 Y=min(ct);
 end
 [T,K]=meshgrid(1:1:600,20);
 figure
 plot(T,ct)
 X;
 Y;
 i=find(X==min(X))
 j=find(Y==min(Y))

[Torsten]

So you try to find T that minimizes C(T) in the interval [1:600] for T ? And where does the K in the denominator of C(T) belong ? Is it the summation index K so that the [ ] had to include the denominator ? And I guess "t" is always "T" ? And "k" is always "K" ?

[lamia]

tryin to find T and K that minimize C(T) , T and k are decision parameters

i guess the approach (my code) is wrong, I struggle with the summation to make the objective function C(T) so i can use fminseach

yes k is alway K ( was a mistake), and t is a variable from the interval T

[Torsten]

K is a summation index in your notation - so it's unclear what you mean by "tryin to find T and K that minimize C(T)".

And what about the summation index K in the denominator of C(T) ?

[lamia]

K is a variable that I didn't know how to define in the script, so I opted for the approach above, in order to find the optimal k and T. but I think it's not the right one

T is the value of the optimal period and K is the number of optimal periods

Answer 1

[Alan Stevens]

Do you mean something like this:

KT0 = [1, 10];  % initial guesses
[KT, C] = fminsearch(@FN, KT0);
K = KT(1); T = KT(2);

disp(['K = ', num2str(K), '  T = ', num2str(T)])

K = 2  T = 108.5802

disp(['C = ', num2str(C)])

C = 1571.1955

function C = FN(KT)
     K = KT(1); T = KT(2);
     cc=15000;
     cp=10000;
     crg=200000;
     rho=0.5;
     eta=56.9;
     beta=2.6;
     alpha=1.63;
     delta=0.015;

     fn1 = @(K,T) ((K.*T-rho*(K-1).*T)/eta).^beta;
     fn2 = @(K,T) (((K-1).*T-rho*(K-1).*T)/eta).^beta;
     fn3 = @(K,T) ((K-1).^(beta-1).*T.^beta)/eta^beta;

     H = @(K,T) alpha*(fn1(K,T) - fn2(K,T)) - delta*beta*fn3(K,T);

     SM = 0;
     for m = 1:K
         SM = SM + H(m,T); 
     end

     C = ((K-1)*cp + crg + cc*SM)./(K.*T);
end

Unfortunately, I think the function has many local minima, so there's no certainty that the above is a global minimum!

[lamia]

thank you, something like this yes

but how to plot the graphs , when I add the curve drawing instructions it doesn't work

[Alan Stevens]

Like this?

KT0 = [1, 10];  % initial guesses
[KT, C] = fminsearch(@FN, KT0);
K = KT(1); T = KT(2);

disp(['K = ', num2str(K), '  T = ', num2str(T)])

K = 2  T = 108.5802

disp(['C = ', num2str(C)])

C = 1571.1955

%  Plot 3d graph
k = 1:20; t = 1:10:200;
nk = numel(k); nt = numel(t);
c = zeros(nk,nt);
for i = 1:nk
    for j = 1:nt
        c(i,j) = FN([k(i), t(j)]);
    end
end
[x,y] = meshgrid(t,k);
surf(x,y,log10(c)),grid
xlabel('T'), ylabel('K'), zlabel('log10(C)')

function C = FN(KT)
     K = KT(1); T = KT(2);
     cc=15000;
     cp=10000;
     crg=200000;
     rho=0.5;
     eta=56.9;
     beta=2.6;
     alpha=1.63;
     delta=0.015;

     fn1 = @(K,T) ((K.*T-rho*(K-1).*T)/eta).^beta;
     fn2 = @(K,T) (((K-1).*T-rho*(K-1).*T)/eta).^beta;
     fn3 = @(K,T) ((K-1).^(beta-1).*T.^beta)/eta^beta;

     H = @(K,T) alpha*(fn1(K,T) - fn2(K,T)) - delta*beta*fn3(K,T);

     SM = 0;
     for m = 1:K
         SM = SM + H(m,T); 
     end

     C = ((K-1)*cp + crg + cc*SM)./(K.*T);
end