The Recurrent Approximation Algorithm in Conditional Optimization Problem

In this paper the conditional optimization problem for table functions is considered. The minimum (maximum) of the function f is to find under restrictions on the function g. The tables of these function values are experimentally obtained. When examining these tables, it's possible to single out areas, supposed to contain the optimal point. When approximating with basis functions by the least squares method the discrepancy decreases with decreasing of these areas. In the limit we obtain the interpolation problem. But when taking into account measuring errors, dispersion of the approximation coefficients estimates increases. The article presents the combined criterion, that takes into account both these factors. The algorithm for finding an area, that satisfies this criterion, is given. As an example the problem of optimizing the properties of the coolant is considered. The function f is the freezing point and the function g is solution viscosity. In this case f and g are functions of two arguments: NaCl concentration and mass fraction of propylene glycol. They are approximated by polynomials of the second degree.