Optimal control
Theorem (Mangasarian)
If U is a convex set and H(t,x,u,p(t))is concave in(x,u)then the
solution of the Maximum Principle above(x(t),u(t))is an optimal
solution of the problem.Theorem (Arrow)
Let
Hb(t,x,p)$maxfH(t,x,u,p)ju 2 Ug
assuming that the maximum is attained. IfHb(t,x,p(t))is concave in x
then if(x(t),u(t))is a solution of the Maximum Principle above then
(x(t),u(t))solves the optimization problem.