How can I write summationn constraints for an optimization problem?

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Ricardo López
Ricardo López 2020-9-29
评论： Matt J 2020-9-29
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!

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Matt J
Matt J 2020-9-29
编辑：Matt J 2020-9-29
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);
  2 个评论
Ricardo López
Ricardo López 2020-9-29
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
Matt J 2020-9-29
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.

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更多回答（1 个）

Ameer Hamza
Ameer Hamza 2020-9-29
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

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