I have a dataset for individual i and time t. I try to find 3 parameters w,a,b to minimize an objective function. Given the parameter values and data, the objective function first compute an optimal decision , then compute the sum of squared difference between and the observed choice X.
That is, I try to do:
When I use fminsearch, it does return reasonable estiamtes around different starting values. The final points also have lower objective values.
However, fminunc always say "Initial point is a local minimum" and the Hessian is all 0s. I've tried (1) other starting values, (2) change the optimality tolerance to 10e-12, but the first-order optimality is 0 at starting values.
Since fminsearch does go to other points with lower objectives, does this mean my objective function isn't actually flat but fminunc just doesn't work well?
I do want to use fminunc to get the Hessian matrix... How can I debug/fix this?