This paper presents an improved method of mine ventilation network optimization in the form of a standard nonlinear programming problem and discusses how the solution speed and accuracy depends on a weight factor introduced in the objective function term of the Lagrangian function. The nonlinear ventilation network problem is posed as one with only equality constraints. This is achieved through the use of slack variables. The methodology adopted in this paper is capable of dealing with the nonlinear convex model with significant savings on computational efforts due to its use of only first derivatives. A MATLAB program has been developed based on the weighted augmented Lagrangian method to optimize a generalized mine ventilation network in order to reduce the overall power consumption of the system. The results obtained with this proposed method matches well with previously published results of the same network problem with significant savings on computational time. It has been shown that a carefully selected weight factor can greatly improve the solution speed and accuracy.