Interior Point Methods in Optimal Control

TL;DR

This paper provides a comprehensive convergence analysis of Interior Point Methods for optimal control problems with state and mixed constraints, including algorithms that do not require strong convexity assumptions.

Contribution

It establishes a complete convergence proof for IPMs in a broad class of OCPs and introduces two new IPM-based algorithms for solving these problems.

Findings

Convergence proven for primal and dual variables without strong convexity.

Development of primal and primal-dual IPM algorithms.

Algorithms applicable to general OCPs with state and mixed constraints.

Abstract

This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results are proved for primal variables, namely state and control variables, and for dual variables, namely, the adjoint state, and the constraints multipliers. In addition, the presented convergence result does not rely on a strong convexity assumption. Finally, this paper provides two IPM-based solving algorithms: a primal solving algorithm and a primal-dual solving algorithm.