Abstract:
The notion of a rank of extremum in the problem of mathematical programming is introduced in this
work. The conditions of the rank extremum for a class of network optimization problems are presented, in
which the correlation between the rank of extremum, its non-locality and the size of the system’s parts
that are to be optimized to get the extremum of the given rank is established. The scheme of two-stage
optimization of network systems is proposed: the global simplified problem is solved at the first stage, the
rank optimization of network system starting from the global solution of the simplified problem is carried
out at the second stage.
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