# A Simple and Efficient Algorithm for Nonlinear Model Predictive Control

arXiv: https://arxiv.org/abs/1709.06487 · HTML: https://mlsanity.com/paper/1709.06487/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2017.

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

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- [Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms](https://mlsanity.com/paper/2306.05815/) (2023)
- [Self-concordant smoothing in proximal quasi-Newton algorithms for large-scale convex composite optimization](https://mlsanity.com/paper/2309.01781/) (2023)
- [A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization](https://mlsanity.com/paper/2409.19428/) (2024)
- [A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints](https://mlsanity.com/paper/2509.02894/) (2025)
- [lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layers](https://mlsanity.com/paper/2609.33630/) (2026)

## Abstract (arXiv)

We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of a quadratic program at every iteration and, consequently, inner iterative procedures. As a result, when the problem is ill-conditioned or the prediction horizon is large, each outer iteration becomes computationally very expensive. We propose a line-search algorithm that combines forward-backward iterations (FB) and Newton-type steps over the recently introduced forward-backward envelope (FBE), a continuous, real-valued, exact merit function for the original problem. The curvature information of Newton-type methods enables asymptotic superlinear rates under mild assumptions at the limit point, and the proposed algorithm is based on very simple operations: access to first-order information of the cost and dynamics and low-cost direct linear algebra. No inner iterative procedure nor Hessian evaluation is required, making our approach computationally simpler than SQP methods. The low-memory requirements and simple implementation make our method particularly suited for embedded NMPC applications.