Strongly and weakly monotone Lyapunov functions and global optimality conditions in control problems
In this report the Hamilton-Jacobi canonical sufficient conditions of global optimality are developed. These conditions are based on using sets of strongly monotone nonsmooth functions of Lyapunov type, which depend on initial or final data. Being solutions of the corresponding Hamilton-Jacobi inequalities, these functions allow us to obtain lower bounds for the cost functionals and sufficient global optimality conditions in optimal control problems. Some applications of weakly monotone Lyapunov like functions are shortly discussed.