My functional model consists of a nonlinear conditional equation of the form
a^x + b^x - 1 = 0
a and b are known. Therefore, I can solve this easily using Gauss-Newton iterations or MATLAB's in-built fsolve function. But: What if I have multiple versions of (a,b) tuples fitting the same model defined by x?
I'd like to solve the resulting overdetermined system by MATLAB's lsqnonlin function, but it of course aims only at minimizing the sum of residuals, whereas I want to minimize the sum of residuals AND the conditional equations be fullfilled. What's the proper proceeding here?