Is it possible to apply a time varying “Factor Exposure” when factor exposure constraint is added?

[GilthasLIU]

By reading the document, I found the B matrix/vector, i.e., the “Factor Exposure Matrix”, seemed to be fixed, if the factor exposure constraint would be applied.

But if I’d like to rebalance the portfolio day by day, it is likely that some of the Factor Exposure Matrices would be time varying as well, e.g., the momentum factor would change by nature. So I don’t know if it is possible to allow the B matrix to be time varying, more specifically, a matrix with row number equal to the row number of the return matrix.

And by the way, I don’t quite understand the necessity of the “Training Period”. What parameters do we need to estimate? Or from another perspective, if all the moments of the return series required in the objective/constrains are given, could I bypass the training period when reblancing the portfolio?

Thanks