Optimizing an unknown function by the method of bounded least squares

Abstract

The problem of estimating the position of an extreme point of an unknown function of several independent variables is examined for the case where the dependent variable is known to be bounded. The classical method of least sequres is formulated as a quadratic programming problem to be solved numerically on a digital computer, where the coefficients of the fitted equation are determined subject to restrictions on both the independent variables and the dependent variable. Several two dimensional models were examined using synthetic experimental design techniques. The results, though not conclusive, indicate that the method of bounded least squares can be a useful computational tool in some two dimensional problems. It remains to be shown whether the algorithm is useful in problems involving more than two independent variables.