GCP-LP: A GPU-CPU Collaborative Framework for Accelerating Large-Scale Sparse Linear Programming

Large-scale sparse linear programming (LP) underpins critical applications in logistics, manufacturing, and scientific computing. However, conventional CPU-only solvers often fail to meet real-time performance demands as problem sizes reach millions of variables and constraints. This paper presents GCP-LP, a GPU-CPU collaborative framework that accelerates the COIN-OR Linear Programming solver by offloading key computational bottlenecks-including sparse matrixvector multiplication (SpMV), pivot selection, and Cholesky factorization-to GPUs while retaining sequential control flow on the CPU. By combining asynchronous data transfer, GPUoptimized memory layouts, and adaptive load balancing, GCPLP achieves up to 10% module-level and 5% overall runtime reductions on NETLIB and Mittelmann benchmarks.