Scaling Decision Optimization to 100 Million Variables and Beyond with mPDLP in NVIDIA cuOpt

Supply chain problems are expanding across more SKUs, lanes, and constraints than ever before, while energy grids are balancing more distributed sources in real time. To meet these challenges, teams need to evaluate larger models and more uncertainty within a practical planning window.

NVIDIA cuOpt GPU-accelerated decision optimization can already deliver speedups of more than 10x over CPU solvers on a single GPU for large-scale linear programming (LP) problems. However, today’s largest planning problems can take hours to converge or exceed the memory capacity of a single GPU. These constraints cause a bottleneck for the workflows that drive business decisions.

Historically, large and notoriously challenging LP problems have been a consistent subject of interest for researchers and practitioners. One such problem, zib03, introduced by Thorsten Koch in 2008 and featuring over 104 million nonzeros, has become a widely studied benchmark for new algorithms and solvers. Figure 1 shows how much progress has been achieved in the field with new algorithms and new hardware for solving this problem. cuOpt is now pushing the limits even further by solving the problem on multiple GPUs with mPDLP, achieving a solve rate nearly 10x faster than a year before.