Function minimization on special computers

For the purposes of discussion, a special computer will be taken to be one in which it is not possible to employ standard mathematical software libraries. Thus we are concerned with the ubiquitous personal computers, various array or pipeline machines, and some mini and micro computers primarily destined to tasks other than general purpose computing (e.g. control applications). The function minimization problem, that of finding a set of parameters <underline>b</underline>* so that S(<underline>b</underline>*) ≤ S(<underline>b</underline>) for all <underline>b</underline> @@@@ <underline>b</underline>* within some region is of interest in many real and contrived problems. The global minimization problem will be addressed only in passing, and attention will be paid mainly to the case where S is continuous and smooth. Brief mention will be made of problems with several constraints on the parameters. However, the mathematical programming problem, where there may be large numbers of constraints, continues to provide a serious challenge to developers of numerical methods for small computers.