# Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problems

arXiv: https://arxiv.org/abs/1804.06539 · HTML: https://mlsanity.com/paper/1804.06539/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2018.

## Built on by (most cited first, 7 of 7)

- [Convex Optimization for Parameter Synthesis in MDPs](https://mlsanity.com/paper/2107.00108/) (2021)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [Task-Guided Inverse Reinforcement Learning Under Partial Information](https://mlsanity.com/paper/2105.14073/) (2021)
- [DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising](https://mlsanity.com/paper/2606.15359/) (2026)
- [Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information](https://mlsanity.com/paper/2106.10533/) (2021)
- [Task-Guided IRL in POMDPs that Scales](https://mlsanity.com/paper/2301.01219/) (2022)
- [Bilinear Mamba-Koopman Neural MPC for Varying Dynamics](https://mlsanity.com/paper/2605.04793/) (2026)

## Abstract (arXiv)

This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex constrained optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm can handle nonlinear dynamics and non-convex state and control constraints. It solves the original problem to optimality by successively linearizing non-convex dynamics and constraints about the solution of the previous iteration. The resulting convex subproblems are numerically tractable, and can be computed quickly and reliably using convex optimization solvers, making the SCvx algorithm well suited for real-time applications. Analysis is presented to show that the algorithm converges both globally and superlinearly, guaranteeing i) local optimality recovery: if the converged solution is feasible with respect to the original problem, then it is also a local optimum; ii) strong convergence: if the Kurdyka-Lojasiewicz (KL) inequality holds at the converged solution, then the solution is unique. The superlinear rate of convergence is obtained by exploiting the structure of optimal control problems, showcasing that faster rate of convergence can be achieved by leveraging specific problem properties when compared to generic nonlinear programming methods. Numerical simulations are performed for a non-convex quad-rotor motion planning problem, and corresponding results obtained using Sequential Quadratic Programming (SQP) and general purpose Interior Point Method (IPM) solvers are provided for comparison. The results show that the convergence rate of the SCvx algorithm is indeed superlinear, and that SCvx outperforms the other two methods by converging in less number of iterations.