ABSTRACT
This chapter is entitled ‘left-overs’ because each of the topics—approximation of derivatives, constrained optimisation and comparison of minimisation algorithms—has not so far been covered, though none is quite large enough in the current treatment to stand as a chapter on its own. Certainly a lot more could be said on each, and I am acutely aware that my knowledge (and particularly my experience) is insufficient to allow me to say it. As far as I am aware, very little work has been done on the development of compact methods for the mathematical programming problem, that is, constrained minimisation with many constraints. This is a line of research which surely has benefits for large machines, but it is also one of the most difficult to pursue due to the nature of the problem. The results of my own work comparing minimisation algorithms are to my knowledge the only study of such methods which has been made on a small computer. With the cautions I have given about results derived from experiments with a single system, the conclusions made in §18.4 are undeniably frail, though they are for the most part very similar to those of other workers who have used larger computers.
