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.
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