A Linear Programming Analogue, a Duality Theorem, and a Dynamic Algorithm

This paper considers fluid analogues for the standard linear programming problem and for a separable nonlinear programming problem. In the former case the usual duality results are demonstrated using the principle of minimum potential energy. In addition by examining the dynamics of the system a new method, referred to as the R-method, is derived for solving linear programmes, although it is not demonstrated that this has any computational advantages over the standard simplex method, except that degeneracy causes no problems. In the nonlinear case the weak Lagrangian principle is derived.

The purpose of the paper is to demonstrate that analogue methods, while being impracticable as a physical method of solving optimisation problems, may give some insight into computational algorithms via dual energy concepts and/or dynamic behaviour.