Matlab function as an objective function in CVX

I want to pass my optimization variable to a Matlab function to evaluate the objective that I want to minimize. For example

  cvx_begin
          variable x(n) % My vaiable
          Energy = Calculate(x,...) % Mttlab function to evaluate the objective function to be evaluated based on the variable x
          minimize(Energy)
          subject to
            0 <= x <= 1
       cvx_end

I read the two topics topic1 topic2 but is not exactly what I want to do. I appreciate if you can help. Thanks.

I did not withdraw my post. Thanks.

Create the function (make it the function you really want, provided it follows CVX 's rules):

function function_output = Calculate(x,p)
function_output = sum((x+p).^2)
end

Use it:

n = 4;  
cvx_begin
   variable x(n)
   Energy = Calculate(x,3) 
   minimize(Energy)
   subject to
   0 <= x <= 1
cvx_end

Does this do what you want? if not, you need to be clearer as to how what you want differs from this paradigm.

Thanks so much for your help. This is what I want. I need to modify my function to match the CVX rules. Now I have an exponential term to be calculated based on the value of x inside the function. How I should write it
p_n = b_n*exp(\frac{a*B_n*f_n}{(t_n*f_n - (A_n*x*C_n)) - 1});
Should I write the expression inside a cvx_begin cvx_end as an unconstrainted optimization?

Error using .* (line 173)
Disciplined convex programming error:
Cannot perform the operation: {positive constant} ./ {real affine}

Error in ./ (line 19)
z = times( x, y, ‘./’ );

Error in * (line 36)
z = feval( oper, x, y );

Error in / (line 15)
z = mtimes( x, y, ‘rdivide’ );

Error in Energy_Sub (line 5)
p_n = (b_n*(exp(aB_nf_n/(t_nf_n - (A_nx*C_n))) - 1));

It might not be convex if x>0. I calculated the second derivative of a simple version of yours:

But if t_n*f_n - (A_n*x*C_n)) - 1 > 0, you can let y==t_n*f_n - (A_n*x*C_n)) - 1 , then express it as exp(a*B_n*f_n*inv_pos(y)) if a*B_n*f_n>0.

Thanks for your help. I have other assumptions on the values so I am sure it is convex. I used your suggestion inv_pos and it works but I have another expression

when I tried to use the same method, it produces a disciplined error. I appreciate if you can help.

Error using .* (line 173)
Disciplined convex programming error:
Cannot perform the operation: {log-convex} .* {convex}

Error in * (line 36)
z = feval( oper, x, y );

Error in Energy_Sub_CVX (line 7)
p_nn = (b_nnexp(aB_nf_ninv_pos(y_n))(exp(aB_nnf_nninv_pos(y_nn)) - 1));

can you show why this is convex?

For the first term, I have a,B_n,f_n,t_n,f_n,A_n,x,C_n >0 and the term t_n f_n - A_n x C_n > 0.
For the second term I have a,B_{n'},f_{n'},t_{n'},f_{n'},A_{n'},x,C_{n'} >0 and the term t_{n'} f_{n'} - A_{n'} x C_{n'}> 0 and the term \exp(\frac{aB_{n'}f_{n'}}{t_{n'} f_{n'}- (A_{n'}xC_{n'})} ) - 1 represents the power in my formulation and I have a constraint that it is greater than zero. I wrote the complete proof for the convexity.

I can’t understand your proof. I don’t know how to express even when it is covex. Let’s consider some very simple cases, try express exp(1/x)*(exp(1/x)-1) first, then exp(1/x)*(exp(1/(x+1))-1).

Still not acceptable by CVX both forms

Screenshot 2022-02-14 161853932×146 5.71 KB

I meaned I can’t even figure out how to express something simple like exp(1/x)*(exp(1/x)-1), let alone b_{n'}*\exp(\frac{a*B_n*f_n}{(t_n*f_n - (A_n*x*C_n))})*(\exp(\frac{a*B_{n'}*f_{n'}}{(t_{n'}*f_{n'} - (A_{n'}*x*C_{n'}))}) - 1)

Thanks so much for your help. I appreciate. I will try to find a numerical search method to use instead of CVX.