3.31.09

Made some incremental progress on the interior point optimization idea but still can't get it to work completely. However, I was able to set the problem up and solve it using CVX, a matlab convex optimization toolbox we used in EE236. Its too black-box to really use for research, but it does spit out a command vector that satisfies the constraints. When the optimal command is applied however, it doesn't really minimize the wavefront variance a tremendous amount, definitely not as much as the PI controller in steady state.

This is probably due to the crappy poke matrix, which has an estimation error around 20%. I get the feeling that the new WFS we have on the way will solve this problem, so I'm putting the interior point idea on the backburner until it arrives. If that doesn't help, another option is to solve the optimization problem for a family of posssible poke matrices. This would still be convex since we're talking about the pointwise maximum of a convex function that is parameterized over a set.

Until then I'm going to continue messing around with the SPGD stuff. I'm learning about some alternative first-order optimization algorithms now that might be interesting to try, since the current gradient descent algorithm appears to be one of the slowest first-order methods out there. It might also be possible to estimate the Hessian of the objective function, allowing the use of a second-order method like Newton's.