GPU-Accelerated Sequential Quadratic Programming Algorithm for Solving ACOPF

Sequential quadratic programming (SQP) is a powerful and widely-used method in solving nonlinear optimization problems, with advantages of warm-starting solutions, high solution accuracy, and quadratic convergence due to the use of second-order information, including the Hessian matrix. In this study, we have developed a scalable SQP algorithm for solving the alternating current optimal power flow problem (ACOPF), leveraging the parallel computing capabilities of graphics processing units (GPUs). Our methodology incorporates the alternating direction method of multipliers (ADMM) to initialize and decompose the quadratic programming subproblems within each SQP iteration into independent small subproblems for each electric grid component. We have implemented the proposed SQP algorithm using our portable and efficient Julia package, ExaAdmm.jl, which solves the ADMM subproblems in parallel on all major GPU architectures. For numerical experiments, we compared three solution approaches: (i) the SQP algorithm with a GPU-based ADMM subproblem solver, (ii) a CPU-based ADMM solver, and (iii) the QP solver Ipopt (the state-of-the-art interior point solver). We observed that for larger instances, our GPU-based SQP solver effectively leverages the many-core GPU architecture, dramatically reducing the solution time.