Variations of gravitation models using geometric programming

The article deals with the gravitation problem, which is widely used for solving different practical problems. First of all it is used to forecast the future traffic of a territory (Origin/destination problem). It is also used in the economy for forecasting the Leontief Input/Output table. It will be shown if the I-divergence is used for the sample O/D matrix and the future traffic matrix the cost function is exponential and the element of the forecasted matrix are determined in the well known RAS form. For the proof the geometric programming and its dual and the week and strong duality theorem are applied.