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

Dayou Luo, Purnanand Elango, Behcet Acikmese

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.

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

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.
Paper Structure (3 sections, 3 theorems, 21 equations)

This paper contains 3 sections, 3 theorems, 21 equations.

Table of Contents

  1. Introduction
  2. Errors and Corrections in citemaoscvx
  3. Proof of Strong Convergence

Key Result

Lemma 2

Given that $\{z \mid J(z) \leq J(z^0)\}$ is compact, iteration $z^k$ is restricted to this compact set and $\psi, G$, and $\nabla G$ are Lipschitz continuous on this compact set.

Theorems & Definitions (7)

  • Lemma 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Remark 5