Non-linear solver with RNN for MPC

Is it possible to use a non-linear solver to optimize the output of a recurrent neural network (RNN) by using a solver to find the optimal RNN inputs?

For example, I want to optimize a RNN to a cost function for the purpose model predictive control. I want to predict future control steps by finding the minimum squared error to a cost function. The solver would iterate the input variables to generate an output at each time step. Part of the RNN output would then be used in the cost function at each time step.

Does anyone have experience using a Python based solver/optimizer on a RNN, especially for the purpose of model predictive control?