This work presents a new method of mine ventilation network optimisation as standard non-linear programming problem and discusses the use of a novel first-order Lagrangian (FOL) algorithm for equality constraints as a solution tool for these problems. Slack variables have been defined to transform such inequality constraints into their corresponding equality forms. The problem is then converted to non-linear problem with equality constrains. The methodology adopted in this paper is capable of dealing with the non-linear convex model with significant savings on computational efforts due to its use of only first derivatives. A MATLAB programme has been developed based on the FOL method to solve a generalised mine ventilation network optimisation problem. To study the validity and the viability of the FOL programme, the programme has been applied to already published network problems and both results are identical.