In this paper, we propose a method for finding an optimum solution of the nonlinear optimization problem with equality constraints. The original problem is replaced by a sequence of unconstrained problems of the augmented Lagrangian function. The subproblems are minimized by using quasi-Newton methods. The Hessian matrix of the augmented Lagrangian is updated by using a new secant approximations which is positive definite at every iteration. A set of computational results on test problems from CUTEr collection are presented.
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