I am doing some Maximum Likelihood Estimation with a density that has time-varying parameters. I am using the fmincon
function in Matlab, but I do not know how to impose restrictions on a vector of parameters. To be clear, I have a vector of parameters (that do not change over time) and I know how to impose restrictions on them. However I want to make two parameters time-varying and I do not know how to impose restrictions on vectors containing those time-varying parameters. Summing up, I have a vector of a few time-invariant parameters and two vectors of time-varying parameters.
I found a paper that suggests using logistic mapping of the form $ \Theta_{t, restricted} = L + \frac{(U-L)}{1+exp(-\Theta_t)}$ where $\Theta_t = (x_1, x_2)$ and U and L are the upper and lower bounds respectively, for the restricted parameter. $x_1, x_2$ are the time-varying parameters on which I want to impose restrictions.
I would be grateful for any help regarding implementing this logistic mapping into my optimization problem.