Minimization of a convex functional in a linear system of delay differential equations with fixed ends

A numerical method is proposed for solving the problem of moving a dynamic object described by a system of linear differential-difference equations to the origin with the minimization of a nonnegative convex functional. The method is proved to converge globally to an $\varepsilon$-optimal solution. The $\varepsilon$-optimal solution is understood as an extremal control $u(t)$, $t\in[0,T]$, that moves the system to the $\varepsilon$-neighborhood of the origin.