How to optimize when the decision variables are complex numbers

Hi, I want to optimize the objective function where and are complex numbers I intend to use genetic algorithm but I wonder if the decison variables (reprsented as complex numbers) can actualy be optimized in matlab.

Best Regards.

[Matt J]

But then your objective function will be complex-valued. How would you define the "maximum" over a list of non-real numbers?

[Saifullah Khalid]

I am completely naive on this issue, so need advice about if it is theoratically sound and also do able.

[Bjorn Gustavsson]

Well you have to answer Matt J's question before proceeding - what do you want for "maximum" of your complex-valued sum? Do you want the maximum real value of that sum, is it the maximum absolute value, or perhaps the maximum imaginary value? Further there ought to be som additional constraints on your optimization parameters (are those or ?).

[Saifullah Khalid]

Bjorn Gustavsson , thank you very much for the reponse and a very helpful insight on the problem. I feel the a maximum absolute value works for me. Now, I need advice about doing it matlab.

My question is, if we have complex decision variables and objective as a maximum absolute value, can we optimize in Matlab (preferably)?

[Bjorn Gustavsson]

Sure, a complex decision variable is nothing more than the sum of 2 real-valued decision-variables - where you multiply one of them with 1i. From there it is just to look at fminsearch or possibly fminsearchbnd or minimize on the file exchange.

[Saifullah Khalid]

@Bjorn Gustavsson once again thanl very much for your support.