Sparse Jacobian Estimation and Factorization on a Multiprocessor
Paul E. Plassmann · 1990
. In this paper we present algorithms and experimental results for the estimation and QR factorization of large, sparse Jacobians on a message-passing multiprocessor. The gist of this work is the development of paradigms for the efficient solution of the "inner loop" of a nonlinear optimization algorithm: the estimation of the Jacobian, its factorization, and the solution of the resulting trust-region problem. A parallel sparse QR factorization based on the global row reduction algorithm is introduced. We emphasize the commonality between row partitions that allow for the efficient parallel factorization of the Jacobian and its estimation. We also note that the interprocessor communication structure constructed for the QR factorization can be used to solve an associated trust-region problem. Finally, experimental results obtained on the Intel iPSC/2 are presented. 1. Introduction. To solve many nonlinear optimization problems it is necessary to estimate and factor the Jacobian of a non...