Infinite-horizon problems under periodicity constraint

TL;DR

This paper investigates infinite-horizon optimization problems constrained to periodic functions, introducing an averaging approach to reduce them to finite horizon problems and deriving existence and optimality conditions.

Contribution

It presents a novel reduction method for infinite-horizon problems with periodicity constraints and establishes existence and optimality conditions involving an averaged Lagrangian.

Findings

Reduction of infinite-horizon problems to finite horizon using averaging

Existence results for solutions under periodicity constraints

Necessary optimality conditions involving the averaged Lagrangian

Abstract

We study so{\`u}e infinite-horizon optimization problems on spaces of periodic functions for non periodic Lagrangians. The main strategy relies on the reduction to finite horizon thanks in the introduction of an avering operator.We then provide existence results and necessary optimality conditions in which the corresponding averaged Lagrangian appears.