Different from the N/LCP formulations, the augmented Lagrangian formulation uses the proximal functions described above, λ λ = p r o j R + ( λ λ − − ρ ρ g ) . Together with dynamics equations, this formulation is solved by means of root-finding algorithms. A comparative study between LCP formulations and the augmented Lagrangian formulation was carried out by Mashayekhi et al.