How to use a constraint on the output of a goal function?

I have an optimization problem where I have 5 variables to optimize. I am using fmincon now wih sqp approach, but in future I may use some other methods as well. The issue is that for some specific combinations of my variables, the goal becomes a complex number, which is not desriable. I was wondering how to avoid these combinations.

For example, if F is my goal I want to set some check to see if F is a real number (and then accept it as a candidate). How can I do it? I have checked the documentation and I have just found setting up a constraint function that works as F <= 0, however I can't think of a clever way to tune this to my complex number problem.

Answer 1

[Torsten]

You must ask yourself: How could the objective function become complex-valued ? Maybe you have a log(x) expression in it and the x became negative ? Or you have an x^a expression in it and the x became negative ?

Once you found the reason, you might be able to set a constraint - either as a lower or upper bound on parameters or in the function "nonlcon" - to avoid this.

[Tworit Dash]

Thank you for the answer. It is indeed a logarithm that goes complex. I know the root cause, but not in the parameter level as this happens probably for some combination of the parameters. And, it is not just a logarithm, it is big sum of logarithms. Inside the logarithm there is a function that is also a sum and inside that sum there are the parameters.

The goal function looks like this:

Here, the Θ are the parameters. In principle for all n should be a positive real number. The problem arises where some of the s go negative. Can I put a constraint that checks for each to be non-negative?

[Torsten]

The first thing I would try is to define the product of the F_n as objective function.

The second thing I would try is to check in your objective function whether all F_n are > 0. If not, return -Inf or NaN (assuming you want to maximize).

The third thing I would try is to define F_n >= 0 for all n in "nonlcon" as constraints.

[Tworit Dash]

I will try the second way; because I want to compute F inside the Goal function. And I can not try the product, because it is kind of a log-likelihood which in linear form is very low in value.