I’m wonder if there is anyway to get the derivate of the optimal solution w.r.t the parameters (preferably from Python interface, C interface is also ok). The eval_param_sens function seems to be able to calculate the sensitivity w.r.t the initial condition, but I’m wondering if more general settings exists, e.g., when parameters appears in the cost function or system dynamics.

we just merged a pull request implementing solution sensitivities with respect to parameters! Note that this feature is currently limited to external costs and discrete dynamics and does not cover parametric constraints.

I recommend you check the example here. Note that the solution sensitivities are only correct if an exact Hessian is used. Whenever you use any form of Hessian approximation or regularization (e.g. Gauss-Newton Hessian) for solving your OCP, we recommend to create two solvers: one for solving using an approximate Hessian, and one using an exact Hessian that is used to compute solution sensitivities. This approach is also taken in the example.