A parallel quasi-Newton method for partially separable large scale minimization

The parallel quasi-Newton method based on updating conjugate subspaces proposed in [4] can be very effective for large-scale sparse minimization because conjugate subspaces with respect to sparse Hessians are usually easy to obtain. We demonstrate this point in this paper for the partially separable case with matrices updated by a quasi-Newton scheme ofGriewank andToint [2,3]. The algorithm presented is suitable for parallel computation and economical in computer storage. Some testing results of the algorithm on an Alliant FX/8 minisupercomputer are reported.The material is based on work supported in part by the National Science Foundation under Grant No. DMS 8602419 and by the Center for Supercomputing Research and Development at the University of Illinois.