ON THE SOLVABILITY OF A NONLINEAR OPTIMIZATION PROBLEM WHEN MINIMIZING A PIECEWISE LINEAR FUNCTIONAL

Abstract

The paper studies the solvability of problems of nonlinear optimization of thermal processes described by integro-differential equations in complex derivatives with an integral Fredholm operator while minimizing a piecewise linear functional. The study was carried out using a generalized solution of the boundary value problem of process control. The integral influence of the operator on the uniqueness of the generalized solution is revealed. The problem of minimizing piecewise linear functionals has specific features and is little studied. On the other hand, the maximum level of the system with different parameters is available. Further, it is established that the conditions in accordance with the uniqueness, the desired unique control should be found as a solution to a nonlinear integral equation and a correspondence to a differential inequality, and this solution should be determined by the sign, i.e. positive or negative over the entire period of time. An algorithm for constructing such a solution to a nonlinear problem has been developed.