Lightening of Assumptions for Pontryagin Principles in Infinite Horizon and Discrete Time

TL;DR

This paper develops Pontryagin maximum principles for infinite-horizon, discrete-time optimal control problems under weaker assumptions than previous work, avoiding continuity, differentiability, and linear independence requirements.

Contribution

It introduces novel Pontryagin principles that require fewer assumptions, broadening the applicability of optimal control theory in discrete time and infinite horizon settings.

Findings

Established maximum principles with weaker assumptions

Avoided need for continuity and differentiability conditions

Reduced restrictions on linear independence

Abstract

In the infinite-horizon and discrete-time framework we establish maximum principles of Pontryagin under assumptions which weaker than these ones of existing results. We avoid several assumptions of continuity and of Fr{\'e}chet-differentiability and of linear independence. MSC 2010: 49J21, 65K05, 39A99.