THE SIMPLEX METHOD FOR MINIMISATION OF A GENERAL FUNCTION

The simplex method is a reasonably fast and efficient procedure for minimising a general function of any number of variables. It operates with function values at a number of points and so can more easily avoid local minima than other methods. It works by constructing a polyhedron and reflecting the point with the highest function value in the centroid of the others. If this results in a lower value, the exploration continues in the same direction; if not the highest point or its reflection is moved towards the centroid. The polyhedron thus moves gradually to lower values until it settles into a minimum. The simplex method contains procedures to deal with special cases and refinements to speed up the process. The report gives the full mathematical statement of the procedure, and the appendix describes a computer program to implement it. The method was developed as part of a research study of long term trends in transport: it is published as a contribution which may find a wider application in the field of mathematical techniques. (Author/TRRL)