Remarks on "Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problems"

TL;DR

This paper critically examines the convergence guarantees of the SCvx algorithm for nonconvex trajectory optimization, identifies errors in prior proofs, and provides corrected convergence proofs under stricter assumptions.

Contribution

It corrects and clarifies the convergence analysis of SCvx, addressing inaccuracies in previous work and establishing more rigorous convergence conditions.

Findings

Identified errors in the original convergence proof of SCvx.

Provided a revised convergence proof under stricter assumptions.

Clarified the theoretical foundations of the SCvx algorithm.

Abstract

The purpose of this note is to highlight and address inaccuracies in the convergence guarantees of SCvx, a nonconvex trajectory optimization algorithm proposed by Mao et al. (arXiv:1804.06539), and make connections to relevant prior work. Specifically, we identify errors in the convergence proof within Mao et al. (arXiv:1804.06539) and reestablish the proof of convergence by employing a new method under stricter assumptions.