Page 86 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.70, # 1, 2013, pp. 77-96

a 2 ,...., a n which meet this requirement are found by the least square method. In

other words, the function below is being minimized:

(4)

Due to the fact that the goal function S is non-linear in respect of parameters a 1, a 2

,...., a n the identification of its minimum faces certain problems during the

application of Ferma theory. Thus the special derivative of function S in respect of

parameters a 1, a 2 ,...., a n and by equation of this derivative to zero finding the

solution of quotation system faces number of the problems and even is not

possible. Therefore the minimization method resolves this problem. We can relate

the Newton – Gauss, Markward, Pauelov and Highbred methods to the method for

minimization of S function.

Let’s introduce the following vectors:

, , , (5)

Now we can show the problem in the following way:

We should find such point a*, which satisfy the following condition: if U=Y-

F function should take the minimal value.

Here, vector - is a transposed vector U.

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