CSE Community Seminar | October 9, 2026

Abstract

Can first-order methods and GPUs solve traditional mathematical optimization problems at scale? For decades, this seemed unlikely: conventional wisdom held that reliable LP solvers depended on simplex or interior-point methods and sparse factorizations, while first-order methods were considered too slow or inaccurate. This talk traces the PDLP research line from CPU-based PDLP through GPU-based cuPDLP to cuPDLPx. I will explain how GPU-friendly sparse matrix-vector operations, restarted primal-dual algorithms, and careful numerical design together achieve high accuracy, robustness, and competitive end-to-end performance. I will also discuss theoretical guarantees for linear convergence and infeasibility detection. Computational results cover standard LP benchmarks and practical applications, including problems with hundreds of millions of variables or nonzeros. Beyond its academic contributions, this line of research has helped drive a broader shift toward GPU-based first-order methods across the optimization solver ecosystem. These methods complement simplex and interior-point algorithms and become especially compelling at very large scales. Time permitting, I will conclude with extensions to convex quadratic and semidefinite programming.