# Linear Programming Formulations of Deterministic Infinite Horizon Optimal Control Problems in Discrete Time

## TL;DR

This paper explores the connection between infinite horizon optimal control problems in discrete time and infinite-dimensional linear programming, analyzing their relationships and asymptotic behaviors for discounted and average criteria.

## Contribution

It establishes a novel link between discrete-time optimal control problems and IDLP formulations, including asymptotic relationships between different criteria.

## Key findings

- Optimal control problems relate to specific IDLP problems.
- Asymptotic relationships between discounted and average criteria are established.
- The study provides a new framework for analyzing long-term control strategies.

## Abstract

This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. We establish that these problems are related to certain infinite-dimensional linear programming (IDLP) problems. We also establish asymptotic relationships between the optimal values of problems with time discounting and long-run average criteria.