On characterizing optimality and existence of optimal solutions for Lyapunov type optimization problems

Abstract

Necessary and sucient conditions for optimality, in the form of a duality result of Fritz-John type, are given for an abstract optimization problem of Lyapunov type. The introduction of a so-called integrand constraint qualication allows the duality result to take the form of a Kuhn-Tucker type result. Special applications include necessary and sucient conditions for the existence of optimal controls for certain optimal control problems.