Reducing the dynamic model of the software development market to a block problem of convex programming

The authors propose to reduce a discrete dynamic model of the software development market to a block problem of convex programming, which can be solved by successive approximations based on contraction mapping, in case of abandoning the integer elements of the destination matrix. However, there are also peculiarities: equilibrium prices can be calculated directly and therefore a variational formulation of the internal problem of determining equilibrium prices based on Debreu's theorem is not required. The functions of phase coordinates’ change can be taken as convex, for example, the norm of the difference squared, and do not take into account the fixed costs for each control switch, which is excluded from the equations of system’s dynamics. The resulting block problem of convex programming allows decomposition by freezing the connection variables with neighboring blocks at the level of the previous iteration. It is shown that the operator on the right side of the resulting recurrent equation is compressive under fairly general conditions. This allows the authors to prove successive approximations for solving the resulting problem, based on the principle of contraction mapping. The authors give the model example of its use in the dynamic expansion of the transport problem according to the value.