# Successive Convexification of Non-Convex Optimal Control Problems and Its Convergence Properties

arXiv: https://arxiv.org/abs/1608.05133 · HTML: https://mlsanity.com/paper/1608.05133/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2016.

## Built on by (most cited first, 11 of 11)

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- [Spacecraft Rendezvous Trajectory Generation with Modular Constraints via Diffusion Model Composition](https://mlsanity.com/paper/2610.05642/) (2026)

## Abstract (arXiv)

This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints are already convex or convexified, the proposed algorithm convexifies the nonlinear dynamics, via a linearization, in a successive manner. Thus at each succession, a convex optimal control subproblem is solved. Since the dynamics are linearized and other constraints are convex, after a discretization, the subproblem can be expressed as a finite dimensional convex programming subproblem. Since convex optimization problems can be solved very efficiently, especially with custom solvers, this subproblem can be solved in time-critical applications, such as real-time path planning for autonomous vehicles. Several safe-guarding techniques are incorporated into the algorithm, namely virtual control and trust regions, which add another layer of algorithmic robustness. A convergence analysis is presented in continuous- time setting. By doing so, our convergence results will be independent from any numerical schemes used for discretization. Numerical simulations are performed for an illustrative trajectory optimization example.