Understanding computation with friction loss

[Gregwar]

Hello,

I am trying to understand the explainations about friction loss computation. In the primal problem, it is expressed as a soft constraint regularized with R with a "Huber" norm.

It is said that Huber norm is accounting for the fact that friction loss forces are kept in their interval. Can someone give me more information on this ?

Is it just a "mind view" of the fact that associated Lagrange multipliers are actually bound in the dual formulation ?

For example, in the case where R is close to 0, it is said that the constraints are getting closer to hard constraints. I understand that since the weight of the constraints violation term is then getting very important. However, this term being quadratic or linear in the error would still be more important than the first term (the Gauss principle one), isn't it ?

(Sorry if this is the wrong place to ask such questions)