"Discontinuity" of dual error in MPC

[abussy-aldebaran]

Hi 👋

I have questions/remarks about how dual error behaves when cycling the problem and the solver, i.e. in MPC mode.

After convergence, the dual error is, for example, 0.01. At the start of the next MPC step, the dual error starts at 10. One might expect to start with a small dual error. I think it stems from the dissymmetry of equations (24) in [1] for t=0 and t=N, which have one term less that other ts. What's more, there is the initial condition constraint.

1. Would it make sense to multiple $\lambda_1$ and $\lambda_N$ by 2 in (24c) and (24d) to restore some symmetry ?
2. Would it be desirable ?
3. What about the initial constraint ?

[1] https://inria.hal.science/hal-04332348v1.