MadSuite: GPU solvers for large-scale optimization

Details: In recent years, the development of scalable continuous optimization solvers on GPUs has made significant progress, primarily driven by advances in GPU-based sparse linear algebra.
We first introduce MadNLP.jl, a GPU-native solver for nonlinear programming (NLP) based on interior-point methods and sparse direct solvers. It was the first solver in the suite and remains central to solving general nonlinear problems efficiently.

Building on this foundation, MadNCL.jl is a robust meta-solver that orchestrates multiple NLP solves to handle degeneracy, ill-conditioning, and to achieve high-accuracy solutions with tolerances below 1e-8.
The latest solver MadIPM.jl, targets large-scale linear and convex quadratic programs (LP / QP).

All three solvers are based on second-order algorithms, enabling robustness and accuracy compared to purely first-order methods.
We present performance results on real-world benchmark instances, demonstrating substantial speedups between CPU and GPU implementations, while maintaining high solution quality.

Audience Takeaway:

• Second-order methods scale on GPUs
• Unified GPU solver suite (NLP / LP / QP)
• Robust, high-accuracy solutions
• Demonstrated real-world CPU–GPU speedups

Zoom: This is a hybrid event. To attend online, join us on Zoom here at 6pm:
https://numfocus-org.zoom.us/j/89399976851?pwd=UEgMUZXdYmKdK1x1dIPL6hwUYnp7NW.1

Sponsors: Illinois Tech Chicago-Kent College of Law will provide the meeting site. Adyen will sponsor snacks for the onsite participants.

• Address: Room 170, Illinois Tech Chicago-Kent College of Law, 565 W Adams St, Chicago, IL 60661, USA.
• Logistics: To access the room, we require first and last names of those who RSVP'd by 6pm on Jan 13. Attendees will then present their IDs when they arrive and sign in at the security desk. All external participants must wear name badges, provided at the registration table.
• Illinois Tech Overview: Illinois Tech is a leading private research university in Chicago, renowned for its programs in Computing, Engineering, and Law. The Chicago-Kent College of Law and the College of Computing are central to the university’s mission of advancing interdisciplinary research and education. The event is hosted in collaboration with Illinois Tech’s Law School and the Department of Applied Mathematics.