Аннотация:A multifaceted methodology for formalizing and solving discrete terminal problems for man-aging dynamic objects under resource constraints is presented. The multifaceted formalism covers all the key elements of the management problem statement, namely: the manage-ment goal, the optimality criterion, and the resource constraints of management. It is based on polyhedral constructions of convex analysis, i.e. polyhedral functions and polyhedral norms. Algorithmization of multi-faceted programming problems is based on the mathemat-ical apparatus and computational methods of linear programming. The proposed method for solving discrete linear speed problems is based on three theoretical structures: prediction of extrapolation of controlled object movements, the principle of immersion of the input opti-mization problem in a number of more algorithmic and simple computational problems, and the mechanism of extreme guidance.