Ranks of extrema and structural optimization of the big network systems

The concept of a rank of non-local extremum of a multiextreme task of mathematical programming is presented. For tasks of optimization of structure and parameters of network systems the condition of a rank extremum in which the interrelation between an extremum rank, its non locality and size of subgraphs of network which optimization is necessary for acquiring an extremum of the set rank is provided. The computing experiment which showed efficiency of a method when designing networks of the 2nd rank of an optimality is made.