The Department of Applied Mathematics, in collaboration with Chicago-Kent College of Law, presents a seminar featuring guest speaker Alexis Montoison, a postdoctoral researcher in the Mathematics and Computer Science division at Argonne National Laboratory, who will present “MadSuite: GPU Solvers for Large-Scale Optimization.” The event will be held at Conviser Law Center downtown (registration required) at 6–7:30 p.m. on Thursday, January 15, 2026, and will also be streamed live on Zoom.

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.

Biography