A. Hantoute
It is shown that the value function of the infinite-variational problems is not so far from being convex. Indeed, we prove the existence of a function with the following properties: It is a value function of some related variational problems (appropriate approximations of the original variational problem), which is convex. This function coincides with the initial function whenever the space is of a finite dimension. More generally, in infinite dimensions, this function also coincides with the original value function on the effective domain of the latter. We show that some topological and algebraic properties of this new function can be used in the derivation of the existence and stability of solutions to the underlying variational problem.
Keywords: Value functions, variational problems, convexity, Lyapunov theorem
Scheduled
GT13.OPTCONT5 Invited Session
November 9, 2023 3:30 PM
HC4: Sacristía Room