Page 88 - Azerbaijan State University of Economics

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

Historically solution for minimization of the function with number of

variables is made based on declining method of gradient. The meaning of this

method is selection of direction of the vector.

Here,

However the direction selected under the gradient method could be far from

the optimal level. In these cases frequenty gives bad combinations. It was

suggested to obtain the accurate vector during the Newton-Gauss procedure by

adding non-negative sign to the diagonal matrix of Liebenberg and Marward (7).

(8)

Here, the parameter -nxn is single matrix. - is any quantity (it maybe equal

to zero) and it is called Marward number.

This method eliminates the shortages of declining gradient and Newton-

Gauss methods.

Thus,

If we came to Newton-Gauss method, in cases when is at higher

value we obtain declining method of gradient:

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