GPU Acceleration in Optimization and Optimal Control

About the Workshop

Optimal control is a fundamental problem in control theory and systems engineering, with applications across process control, autonomous systems, and energy systems. As these applications grow in complexity, the underlying optimization problems become increasingly large-scale and computationally demanding, and traditional CPU-based solvers often struggle to meet real-time requirements.

While GPUs are best known today as the workhorse of large-scale AI model training, the same hardware is highly effective for the numerical computations at the heart of control — and its usefulness extends well beyond training neural-network policies. Modern GPUs deliver an order of magnitude more arithmetic throughput and memory bandwidth than CPUs, and recent advances now make it possible to bring this performance to bear on the structured nonlinear programs that arise in optimal control. By exploiting the repeated structure induced by time-discretized dynamics, GPU-accelerated interior-point methods can solve problems faster, scale to far larger horizons and state dimensions than CPU-based solvers, and open the door to real-time control of systems that were previously out of reach. This workshop bridges the gap between these algorithmic advances and the practitioner, providing both the theoretical understanding and the hands-on skills to formulate and solve large-scale problems efficiently on modern GPU architectures.

Format: Half-day (3.5 hours, including a coffee break). About 2 hours of lectures on theoretical foundations and algorithms, followed by about 1.5 hours of hands-on tutorials with interactive notebooks.

Organizer

Sungho Shin

Texaco–Mangelsdorf Career Development Chair Assistant Professor
Department of Chemical Engineering, Massachusetts Institute of Technology

Sungho Shin works on GPU-accelerated nonlinear optimization for large-scale optimal control. He is the lead developer of MadNLP.jl, a GPU-accelerated interior-point solver for nonlinear programming, and ExaModels.jl, an algebraic modeling and automatic differentiation tool for GPUs. His group's recent work shows that GPU-resident interior-point methods can deliver order-of-magnitude speedups on optimal-control-style nonlinear programs that arise in process control, autonomous systems, and power-grid operations.

The MadNLP and ExaModels team received the COIN-OR Cup (2023) for outstanding contributions to open-source operations research software, and the group's work on AC optimal power flow on GPUs was highlighted on the NVIDIA technical blog (2024).

Web: shin.mit.edu · Email: sushin@mit.edu · Google Scholar · GitHub

Topics & Audience

Part 1 — Foundations & algorithms

Introduction to nonlinear optimization and software tools. Fundamentals, building toward optimization formulations of optimal control:

Constrained nonlinear optimization: optimality conditions and the role of structure.
The interior-point method.
Nonlinear optimal control via direct transcription.
Collocation methods.

Recent advances in GPU-accelerated optimization. What's new and what makes it work on the GPU:

GPU computing: architectures and basic algorithms.
Direct sparse linear algebra on GPUs.
Condensed-space interior-point methods.
Variants and recent extensions.

Part 2 — Hands-on tutorials

GPU computing in the Julia language. Implementing GPU code from the basics:

Array programming — largely automatic in Julia via broadcasting on GPU-resident arrays.
Kernel programming with CUDA.jl and KernelAbstractions.jl.

Formulating and solving nonlinear optimal control problems on GPUs. Using the MadSuite tooling:

Formulating problems with ExaModels.jl.
Solving them with MadNLP.jl.
A first nonlinear optimal control example, end to end.

Extensions: parameter estimation and energy systems. More involved examples that build on the same modeling and solver stack:

Parameter estimation for dynamic systems.
Energy-system applications (e.g., AC optimal power flow).

Example applications are drawn from nonlinear model predictive control in process control, autonomous systems, and energy systems. A similar tutorial — focused on power systems — was offered at PowerTech 2025; the IFAC 2026 edition retargets the material to optimal control.

Audience & outcomes

The workshop targets researchers and practitioners in control, optimization, and systems engineering, as well as graduate students and postdocs working on optimal control and model predictive control. It is also relevant to anyone interested in high-performance computing for control in process control, autonomous systems, and energy systems.

By the end of the workshop, participants will be able to:

Formulate large-scale optimal control problems as structured nonlinear programs.
Identify and exploit problem structure suitable for GPU acceleration.
Use modern modeling tools and GPU-accelerated interior-point solvers on their own problems.
Adapt the provided example codes and modeling templates to their own research.

Prerequisites

Basic background in optimization and control (nonlinear programming, optimal control, MPC).
Basic programming experience with a high-level scientific computing language (Julia or Python). Julia is used in the hands-on tutorials; introductory material will be provided.
No prior GPU programming experience required — the workshop focuses on high-level modeling and algorithmic concepts.

Schedule & Logistics

Date: Sunday, 23 August 2026 (pre-congress day, immediately preceding the IFAC World Congress on 24–28 August 2026).
Venue: BEXCO, Busan, Republic of Korea — in conjunction with the 23rd IFAC World Congress.
Duration: Half day (3.5 hours).
Language: English.
What to bring: A laptop with a modern web browser. Hands-on examples will be provided as notebooks and can be run on a hosted environment; local installation instructions for Julia, ExaModels.jl, and MadNLP.jl will be made available before the workshop. Access to a GPU is not required — a shared GPU environment will be provided for the live exercises.
Materials: Lecture slides, notebooks, and example code will be linked from this page and from a public repository in advance of the workshop.
Registration: Handled through the IFAC 2026 World Congress system. The workshop is part of the pre-congress workshops program and is available to regular congress registrants (Full, Student, One-day Industry, or Retiree). Early-bird deadlines will be announced on this page.
Code of conduct: Participants are expected to follow the IFAC Code of Ethics and Conduct.
Contact: For questions about workshop content, contact sushin@mit.edu.

Tentative Schedule

All times in Korea Standard Time (KST, UTC+9). Workshop runs 08:30–12:00.

Time (KST)	Session
08:30–08:35	Logistics
08:35–09:25	Introduction to nonlinear optimization and software tools
09:25–09:30	Short break
09:30–10:20	Recent advances in GPU-accelerated optimization
10:20–10:40	Morning coffee break (fixed)
10:40–11:05	GPU computing in the Julia language interactive
11:05–11:30	Formulating and solving nonlinear optimal control problems on GPUs interactive
11:30–11:55	Extensions: parameter estimation and energy systems interactive
11:55–12:00	Closing

Software & Papers

Software stack

The workshop is built on the following foundational stack:

Julia

High-performance scientific computing language

The base language for all examples and packages used in the workshop.

julialang.org →

CUDA.jl

CUDA programming for Julia

Provides Julia bindings to NVIDIA CUDA, including GPU arrays, kernel programming, and core numerical libraries.

github.com/JuliaGPU/CUDA.jl →

KernelAbstractions.jl

Vendor-agnostic GPU kernel programming

Lets the same kernel run across CUDA, ROCm, oneAPI, and Metal back ends, used throughout the MadSuite tooling.

github.com/JuliaGPU/KernelAbstractions.jl →

On top of this stack, the hands-on portion uses two packages from MadSuite, an open-source optimization software suite for GPUs developed and maintained by the organizer:

ExaModels.jl

Algebraic modeling & automatic differentiation for GPUs

An algebraic modeling and automatic differentiation tool for GPUs, generating sparse Jacobians and Hessians of structured nonlinear programs for efficient GPU execution.

github.com/exanauts/ExaModels.jl →

MadNLP.jl

GPU-accelerated nonlinear programming solver

Interior-point method for large-scale nonlinear programs, with GPU-resident KKT solves for structured problems.

github.com/MadNLP/MadNLP.jl →

Selected papers

The workshop draws on the following papers, which together cover the algorithmic foundations and software design of GPU-accelerated nonlinear optimization. A more complete list is available on the organizer's publications page.

S. Shin, F. Pacaud, M. Anitescu. Accelerating optimal power flow with GPUs: SIMD abstraction of nonlinear programs and condensed-space interior-point methods. Electric Power Systems Research, 2024. [arXiv:2307.16830] [doi]
F. Pacaud, S. Shin, A. Montoison, M. Schanen, M. Anitescu. Condensed-space methods for nonlinear programming on GPUs. 2024. [arXiv:2405.14236]
F. Pacaud, M. Schanen, S. Shin, D. A. Maldonado, M. Anitescu. Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures. Optimization Methods and Software, 2024. [arXiv:2301.04869] [doi]
F. Pacaud, S. Shin. GPU-accelerated dynamic nonlinear optimization with ExaModels and MadNLP. 63rd IEEE Conference on Decision and Control (CDC), 2024. [arXiv:2403.15913] [doi]
F. Pacaud, S. Shin, M. Schanen, D. A. Maldonado, M. Anitescu. Accelerating condensed interior-point methods on SIMD/GPU architectures. Journal of Optimization Theory and Applications, 2023. [arXiv:2203.11875] [doi]
A. Montoison, F. Pacaud, S. Shin. GPU implementation of second-order linear and nonlinear programming solvers. NeurIPS Workshop on GPU-Accelerated and Scalable Optimization, 2025. [arXiv:2508.16094]
D. Cole, S. Shin, F. Pacaud, V. M. Zavala, M. Anitescu. Exploiting GPU/SIMD architectures for solving linear-quadratic MPC problems. American Control Conference (ACC), 2023. [arXiv:2209.13049]