How can I write summationn constraints for an optimization problem?

Good morning,

I would like to optimize the following equation:

min

with the following contraints:

x>0

Where is a known set of values, is equal to a [288x1] vector and is also known as a [288x1] vector.

How can I add those constraints? I am trying to use x=fmincon(fun,x0,A,b,Aeq,beq);

Thanks!

[Ricardo López]

I would like to get the optimum x_i as a [1x288] vector.

Answer 1

[Matt J]

fmincon is not the best tool to use for a linear program. In the problem-based framework, you can set up the problem to be solved with linprog() as follows:

x=optimvar('x',size(c),'LowerBound',0);

prob=optimproblem('Objective',x.'*price);
prob.Constraints.sumx=sum(x-c)==0;

sol=solve(prob);

[Ricardo López]

Thanks! that works but it gives just one minimum. is electricity consumption and price is the price at every time i. I would like to re-locate that consumption in a "real" way. Not just finding a minimum in price and consume everything there.

Idk if I shoud add more constraints then, but it worked with the optimization tool in Matlab. Thing is, I would like to have or understand the code behind it.

Thanks!

[Matt J]

Thing is, I would like to have or understand the code behind it.

TMW will not provide the code, but there are algorithm descriptions here

https://www.mathworks.com/matlabcentral/answers/601843-how-can-i-write-summationn-constraints-for-an-optimization-problem#comment_1029715

It sounds like we have answered your original question, so I encourage you to Accept-click the answer. If you have spin-off questions, it would be best if you pose them in a separate thread.

Answer 2

[Ameer Hamza]

Something like this

price = rand(288, 1); % example value
c = rand(288, 1); % example value
sum_c = sum(c);

x0 = rand(288, 1); % initial guess
fmincon(@(x) price.'*x, x0, [], [], [], [], [], [], @(x) nlcon(x, sum_c)) % price.'*x is same as sum(price.*x)

function [cneq, ceq] = nlcon(x, sum_c)
    cneq = [];
    ceq = sum(x) - sum_c;
end