Simultaneous Solving of Batched Linear Programs on a GPU

Abstract

Linear Programs (LPs) appear in a large number of applications. Offloading the LP solving tasks to a GPU is viable to accelerate an application's performance. Existing work on offloading and solving an LP on a GPU shows that performance can be accelerated only for large LPs (typically 500 constraints, 500 variables and above). This paper is motivated from applications having to solve small LPs but many of them. Existing techniques fail to accelerate such applications using GPU. We propose a batched LP solver in CUDA to accelerate such applications and demonstrate its utility in a use case - state-space exploration of models of control systems design. A performance comparison of The batched LP solver against sequential solving in CPU using the open source solver GLPK (GNU Linear Programming Kit) and the CPLEX solver from IBM is also shown. The evaluation on selected LP benchmarks from the Netlib repository displays a maximum speed-up of 95x and 5x with respect to CPLEX and GLPK solver respectively, for a batch of 1e5 LPs.