Batched Second-Order Adjoint Sensitivity for Reduced Space Methods

Abstract

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic differentiation (AutoDiff) backend that targets highly parallel architectures by extracting the second-order information in batch. When the nonlinear equations are associated to a reduced space optimization problem, we leverage the parallel reverse-mode accumulation in a batched adjointadjoint algorithm to compute efficiently the reduced Hessian of the problem. We apply the method to extract the reduced Hessian associated to the balance equations of a power network, and show on the largest instances that a parallel GPU implementation is 30 times faster than a sequential CPU reference based on UMFPACK

Condensed interior-point methods: porting reduced-space approaches on GPU hardware

“…Hence, we avoid computing the full sensitivity matrix S and rely instead on a batched variant of the adjoint-adjoint algorithm [28]. First, we compute an LU factorization of G x , as P G x Q = L U , with P and Q two permutation matrices and L and U being respectively a lower and an upper triangular matrix (using SpRF, the factorization can be updated entirely on the GPU if the sparsity pattern of G x is the same along the iterations).…”