Optimal solutions for a class of infinite horizon variational problems with extended-valued integrands

Abstract

In this work, we study the structure of optimal solutions of infinite horizon autonomous variational problems with a lower semicontinuous integrand f : R ⁿ  × R ⁿ  → R ¹ ∪ {∞}, where R ⁿ is the n-dimensional Euclidean space. We also show that all the optimality notions used in the literature are equivalent for the problems with the integrand f.

Keywords:

• good function
• infinite horizon
• overtaking optimal program
• turnpike property

Mathematics Subject Classification 2000::

• 49J99