How can I formulate, in mixed integer programming (a set of constraints), the following issue:
I have a maximization function on x, g(x).
I need to convert a continuous linear function on x, f(x) (with x real) such that when f(x)=0 it passes f(x).
Thanks in advance,
Diogo
Diogo
Your question is not very clear, but I believe that your problem can be easily solved by Linear Programming
If you want, send me the problem for me to study it in depth, I will be happy to help if I can
To clarify:
How can I formulate in mixed linear programming (a set of constraints) the following issue. I have a maximization function on x, g(x). I need to convert a continuous linear function on x, f(x) (with x real) such that when f(x)=0 it passes f(x).
I have the indicator constraints formulated as
y >= f(x)/M y = 0 then g(x) = f(x)
with
g(x) >= 0
Any guidance on this?
Hopefully, this one might help.
https://orinanobworld.blogspot.com/2011/01/max-and-min-functions-in-mip.html
Technically, it is going to depend on whether f(x) is passed into the objective function with positive or negative sign, and on some available lower and upper bounds for f(x).
Though, formally you can write in the objective function:
the "positive part function" for f(x). (the so-called shortfall function)
https://mathworld.wolfram.com/PositivePart.html
which is, however, usually minimized in finance and insurance.
Technically, you have it: with the binary variable y = 0 or y = 1, your constraints guarantee that g(x) = f(x) if y=1; otherwise, if y = 0 and we are interested in maximum for g(x) = f(x) then g(x) = 0.
Or, I am something here!?
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