An efficient parallel scheme for minimizing a sum of Euclidean norms

Abstract

The problem of minimizing a weighted sum of Euclidean norms is considered. Applications include minimal-surface computations. A robust parallel algorithm, based upon a line-search Newton's method, is presented which takes full advantage of the structure of the problem in order to fully utilize vectorization and concurrency in the computations. The proposed method can achieve good performance, especially on a machine with an architecture that combines vector and parallel capabilities on a two-level shared memory structure such as that on the Alliant FX/8 system. Performance results are given on the Alliant to illustrate the efficiency of the algorithm.