Solvin Unit Commitment Problem with Matlab and the Cplexmilp Function

Hello,

I am trying to solve a Unit commitment problem with Matlab and the cplexmilp function. The objective consists in minimizing the total cost over a certain horizon. The cost is determined with equation (1) from the document. Using Matlab, this problem has to be solved with a matrix and not with the sum function. A row of the Matrix represents one specific time step (correct me if I am wrong).

Further boundaries are expressed with a separate matrix. The question I have is how to implement formulations, where information of the prior time steps are required i.e. (equation (1)).

Does it matter if I use an explicit or implicit Euler approach to discretize a first order derivative of a continuous variable when it comes down to solve MILP problems?

Thanks a lot for your support.