The paper of H.Z. Luo, X.L. Sun, Y.F. Fu and H.X. Wu is located in the area of mathematical programming where optimization theory meets with the solution of complementarity conditions. In fact, it deals with, among other restrictions, complementarity condition constrained nonlinear optimization. Such conditions can nowadays often be found in the applications, e.g., by duality, game, equilibrium (Hamiltonian, etc.) or other geometric kinds of motivations. Historically, a motivation for them consisted in corresponding optimality conditions of first order (for classical nonlinear programs underlying), which gave rise to a new solution technique for the regarded problems, exploiting the multiplicative nature of equality constraints accompanied by nonnegativity conditions on the factors. By the use of a so-called NCP function, the latter conditions becomes ``absorbed'' and, hence, disappears in the problem reformulation. This paper is of a numerical nature, but also of a theoretical one that is necessary for the numerics. The present paper presents new concergence results of augmented Lagrangian methods for mathematical programs with complementarity constraints (MPCC). For the reformulation of MPCC as a constrained nonconvex optimization problem, the authors consider modified augmented Lagrangian methods based on four different algorithmic strategies. They show that the convergence to a global optimal solution can be ensured without a boundedness conditition on the multipliers. This article is well written and well structured, it advances science, and it can also serve as a prepatation of modern applications and future research. The paper consists of Section 1 on introduction, Section 2 on two classes of augmented Lagrangian functions, of Section 3 on a basic primal-dual scheme, Section 4 on modified augmented Lagrangian method using safeguarding, Section 5 on modified augmented Lagrangian method with conditional multiplier updating, Section 6 on penalty parameter updating and normalization of multipliers and, finally, of Section 7 on concluding remarks.