Reduction of route optimization problems

Sequential reaching of a finite system of sets with an additive cost aggreg ation function is studied. The representation of the extremum for the trave lling salesman problem when the "cities" vary within the limits of sets is investigated. For displacement costs defined by a seminorm, the work domain of the dynamic programming method is reduced through the substitution of t he initial set of boundaries, which in concrete problems is discretized. Wo rsening of the extremum is estimated by the sum of Hausdorff deviations. A model example is given.