Remarks on the numerical solution of certain linear complementarity problems

In a recent paper, J.K. Aitchison and N.K. Upton have proposed a mathematical model of the behaviour of a cloud formed immediately after the sudden release of a pollutant, together with an algorithm for determining numerical solutions of the resulting system of constrained nonlinear equations and complementarity relations. This algorithm requires, at each step, the solution of a special linear complementarity problem, which is solved by an iterative method. In this note, it is argued that the robustness and reliability of the solution procedure can be improved by the use of standard linear programming techniques.