Optimization while limiting the number of design variables

A new approach to the formulation and solution of optimization problems of linear and nonlinear type is stated in this article. The problem statement under consideration differs from the classical linear programming problem of the opti- mal distribution of limited resources between given processes by the need to choose a limited number of processes from a certain finite set and allocate resources over these processes. The goal is to obtain the optimal value of the objective function in relation to other options for choosing the number of processes from the same set and the distribution of re- sources between them. The objective function can be either linear or non-linear. A nonlinear function must have certain properties for the correct operation of the proposed algorithm for finding the optimal solution. The described method is based on the development of Bellman's ideas of dynamic programming. The proofs of the optimality of the obtained solutions are provided. The article gives an estimate of the computational complexity of the algorithm and a comparison with classical methods for solving the problems under consideration. The types of applied problems solved using the proposed method are characterized. Computer implementations of the described algorithm can be used in automated decision support systems.