We first introduce the penalty method as a tool for reducing the equality-constrained quadratic programming problem to an unconstrained one and show that increasing the penalty enforces the reduced feasibility error. Then, we apply the penalty method to the augmented Lagrangian and show that we can achieve the same feasibility error without penalization using a suitable value of Lagrangian multipliers. We examine the convergence of the resulting augmented Lagrangian method with the exact solution of auxiliary problems.