Optimisation of Mine Ventilation Networks Using the Lagrangian Algorithm for Equality Constraints


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.


Mining Engineering

Keywords and Phrases

Algorithms; Constraint theory; Lagrange multipliers; Mine ventilation; Nonlinear programming; Optimization; Equality constraints; First order; Inequality constraint; Mine gases; Mine ventilation network; MSHA regulations; Nonlinear programming problem; Ventilation network; MATLAB; First-order Langrangian algorithm; Non-linear programming; Ventilation network optimization

International Standard Serial Number (ISSN)

1748-0930; 1748-0949

Document Type

Article - Journal

Document Version


File Type





© 2015 Taylor & Francis, All rights reserved.

Publication Date

01 May 2015