Letter to the Editor—-A Closed Form Solution of Certain Programming Problems

Abstract

A formula is given for the coordinates of the point that maximizes a given function F ( x 1 , …, x n ) over the closure of a bounded domain S in n -dimensional Euclidean space. The principal assumption made in deriving the formula is that F attains a global maximum at exactly one point of S . In certain cases the formula may be used to discuss the maximization problem as a function of the parameters involved. Some simple examples are given.