CONSTRAINTS AND DUALITY
E. N. Makhmudov · 1992
I (x (.), tl) = (9 (x (t,), tl) + j to g (x (t), t) dt -~ in f, z(t)~a(x(t), x(t--h),t), t~(to, tl), z(t)=~(t), t~(to--h, to), .r(q)~M, x (t) ,~ F (t), t ~ (to, t j), Formulation of the Problem. In this note, we consider a Bolza-type problem for In Sec. 3, for the convex problem we prove duality theorems and show that the adjoint differential inclusion plays the role of the extremal relation for the primary and the dual problems. In (3-7) similar problems for various differential inclusions without effect of delay have been studied well. To construct the dual problems, a convex continuous problem is replaced by a discrete-approximation problem and results from (8) are used. However, we do not give these computations here.