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Abstract. In this contribution an iterative method for solving the nonlinear minimization problem with equality constraints is presented. The method is based on the sequential minimization of the differentiable penalization function known as augmented Lagrangian. Each unconstrained minimization subproblem is solved by using a conjugate-gradient technique combined with a trust-region strategy of globalization, which is especially efficient for large-scale problems. The update of the multipliers and the penalty parameter is done by using standard schemes. The theoretical properties and the behavior of the algorithm are discussed. Details of the implementation are presented, the algorithm is tested with a set of classic problems and with a minimax formulation to the problems which belong to the well known family of Hard-Sphere Problems.

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