The paper is devoted to the problem of the optimization of the dynamics of intensive beams of charged particles in accelerating and focusing structures. A mathematical model of mutual optimization of program and disturbed motions of beam of interacting particles is suggested. This mathematical model includes integral-differential equations that in essence are analogs of Vlasov equations allowing to take into consideration interactions of particles and thus to determine self-consistent motion of charged particles beam in external field. Parameters of accelerating and focusing fields is necessary to determine as a result of the optimization of functionals characterizing charged particles beam dynamics. The paper examines a variation of a functional based on the approaches of theory of optimal control. Analytical representation of the representation of the first variation with use of auxiliary (conjugated) functions is found and optimality conditions in the form of principal of maximum by Pontryagin are formulated.