Nonlinear Optimization problem ( If statement)

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michael francesco pez
评论： michael francesco pez 2020-4-28
Hello everyone,
I'm tryng to solve a nonlinear optimization problem (constrained) using fmincon with 2232 variables (three vectors x,y,z of 744 elements).
I would like to add an "if condition" to the costraints, something like this:
for i=1:744
if x(i)>=650
y(i)<100
else
y(i)<50
end
end
it gives me the following error message :
"Conversion to logical from optim.problemdef.OptimizationInequality is not possible."
How can I add that kind of constraint?Is it possible with fmincon? If not, what solver would be the best choice?
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michael francesco pez
michael francesco pez 2020-4-24
X and Y are vectors of 744 elements. The for and the if loops,together, set the constraint of each element of X. If the element Y(i) is above 650, the constraint on X(i) is X(i)<100; if y(i) is less than 650, the constraint is X(i) <50
Ameer Hamza
Ameer Hamza 2020-4-24
You mentioned that you get this error
"Conversion to logical from optim.problemdef.OptimizationInequality is not possible."
Can you show the code which cause this error?

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Matt J
Matt J 2020-4-24
编辑：Matt J 2020-4-24
To do that, each x(i) must have finite upper and lower bounds L(i)<=x(i)<=U(i). You also need to introduce additional unknown binary variables b(i) and express your constraints with the following linear inequalities,
b(i)>=(x(i)-650)/(U(i)-650) + eps %Forces b(i)=1 when x(i)>=650
b(i)<=(x(i)-L(i))/(650-L(i))-eps %Forces b(i)=0 when x(i)<650
y(i)<=50+50*b(i)
Since fmincon does not allow integer variables, you will need to use ga or intlinprog instead.
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Walter Roberson
Walter Roberson 2020-4-28
Logically speaking, you cannot know that you have found the minima unless you have tested both sides of each discontinuity. With 774 variables each with a discontinuity, then logically speaking you cannot know that you have found the minima without at least 2^774 function calculations.
This number could potentially be drastically reduced if you could partition the system into linear combinations of subproblems that you can minimize independently.
michael francesco pez
michael francesco pez 2020-4-28
Ok, so there is no way to make it faster. I got it.
If no other solver can handle this kind of problem (many variables, integer and continuous variables, non-linear constraints), I'll try to change it a little bit to make it easier.
Thank you for the answers!

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