My function is nonlinear with respect to a scalar \alpha .
However, the calculation of objective function is very time consuming, making optimization also very time consuming. Also, I have to do it for 1/2 millon voxels (3d equivalent of pixels). I plan to do it using “lsqnonlin” of matlab. However, this question is purely mathematical.
Rather than optimizing over all possible real values, I plan to search over preselected 60 values. Since I can pre-calculate value for these, it would be very fast. In other words, I need to restrict search space.
I can not do grid search over preselected value as I plan to perform spatial smoothing in 3D. Some guidance would be highly appreciated.
Regards, Dushyant