fmincon optimization of airfoil, gradients

Hi,

I am trying to perform numerical optimization of an airfoil using the gradient solver fmincon in the optimization toolbox in MatLab.

I have problems understanding how to calculate the gradients. At the moment I approximate the derivatives by perturbing the vector controlling the creation of the airfoil using forward differencing applied in the MatLab toolbox.

Even though I only optimize for a single Cl value, I need to solve a range of Cl values with small step sizes around the point of interest, due to convergence problems in the flow solver (XFOIL), spline fit the data and interp1 my optimization point. And this is where the problem occurs I think. I only want to calculate the gradient for the point of interest. Not for all the other Cl values I compute in XFOIL. Still, fmincon computes the gradients for all cl values, and gets confused. Next, I want to compute the full Cl-alpha curve in XFOIL, but I still only want to optimize the airfoil (and therefor compute the gradients) at some specific points of interest.

Is my understanding of the problem correct? How do I make fmincon do what I want?

I normally use GA and PatternSearch for my optimization, and have no problems with these gradient free methods.

Regards, Thomas

Answer 1

[Alan Weiss]

The documentation on optimizing a simulation or ODE might help. In particular, look at the suggestion for finite differences, and try central finite differences, too.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation