Parametric decomposition of the multi-phase transport models

Flighted transport models occupy a special place among the problems of mathematical programming. With granular approach to their solution, describing the elementary acts of administrative activity, there arises the problem of the extremum of algorithmic functions on the set of algorithmic restrictions in the conditions of high dimensionality of the space of variables. Given that multi-stage transportation problem has a block structure with a small number of links, it makes sense to use such decomposition schemes that lead to the problem of minimizing nonsmooth convex piecewise-linear function of the related parameters, relevant constraints of the problem in a binder. The most promising and appropriate for solving such problems is the approximate analytical description of the object of management and development of approaches for solving the problem of finding an extremum algorithmic functions on the set of algorithmic constraints in high dimensional space of the variables of the problem and the limited time calculations. In such cases, it makes sense to use a parametric decomposition associated with nonsmooth optimization problems of convex functions, multi-phase transport models. The article considers the application of the algorithm steepest descent algorithm for solving such problems.