GPU Accelerated Parallel Implementation of Linear Programming Algorithms

Linear Programs are computationally expensive for large constraint matrices. Existing linear programming solvers use serial mode processing using Central Processing Unit (CPU) computation that leads to long execution runtime in real-time. This paper presents, parallel implementation of the Simplex and Interior Point Method using General Purpose Graphical Processing Unit (GPGPU) empowered with a novel Compute Unified Device Architecture (CUDA) for solving multiple LP problems simultaneously. The methods are accomplished by using the concept of parallel kernel map of the algorithms through multiple CUDA threads. The algorithms are implemented in NVIDIA A40 GPU model. The runtime of the algorithms is compared with the standard Scipy linprog solvers for the above methods. We also demonstrated the superior performance of the implemented algorithms by varying the size of the linear programming problem.