How to solve non-linear equations having modulus expression?

Hi

I am trying to solve a set of non-linear equations with the final expression in the form of:

power=(abs(non-linear equation))^2;

My system is such that I only have access to the value after modulus of the expression. Therefore, I can not solve the expression by comparing the real and imaginary part.

Is there any way to solve this problem in matlab?

Thanks!

Answer 1

[Ameer Hamza]

See lsqnolin(): https://www.mathworks.com/help/optim/ug/lsqnonlin.html.

Or fmincon(): https://www.mathworks.com/help/optim/ug/fmincon.html for a more general solution.

[Anuj Kumar Sahoo]

Hi Ameer

lsqnonlin() and fmincon() are working perfectly as long as I am comparing the real and imaginary part of the expression, before taking the modulus. Unfortunately, in practice I only have access to the power term i.e. (mod(expression))^2. For which I am facing problem.

FYI: I have also tried expressing

abs(a)^2 == a.*conj(a)

But it didn't work as well.:(

Answer 2

[Alan Weiss]

As long as you have no bounds, you can use lsqnonlin directly. See Fit a Model to Complex-Valued Data.

Alan Weiss

MATLAB mathematical toolbox documentation

[Anuj Kumar Sahoo]

Hi Alan

Thanks a lot for your suggestion. But I think my problem still is the unavoidable "modulus" expression in my equation which is stopping me from getting correct answer. The link you shared was definitely useful, but didn't serve my purpose in this case. May be this technique will be helpful to me in some other problem.

Regards