MINPACK

Abstract: The Army High Performance Computing Research Center at the University of Minnesota and the Mathematics and computer Science Division at Argonne National Laboratory have initiated a collaboration for the development of the software package MINPACK-2. As part of the MINPACK- 2 project, we are developing a collection of significant optimization problems to serve as test problems for the package. This report describes some of the problems in the preliminary version of this collection. Optimization software has often been developed without any specific application in mind. This generic approach has worked well in many cases, but as we seek the solution of larger and more complex optimization problems on high-performance computers, the development of optimization software should take into account specific optimization problems that arise in a wide range of applications. This observation was the motivation for the main requirement for inclusion in this collection: each problem must come from a real application and be representative of other commonly encountered problems. Problems in the preliminary version of the collection come from such diverse fields as fluid dynamics, medicine, combustion, nondestructive testing, chemical kinetics, lubrication, mathematics, and superconductivity.

Abstract: The authors recently proposed a new parallel algorithm, based on the sequential Levenberg–Marquardt method, for the nonlinear least-squares problem. The algorithm is suitable for message-passing multiprocessor computers.In this paper a parallel efficiency analysis is provided and computational results are reported. The experiments were performed on an Intel iPSC/2 multiprocessor with 32 nodes: this paper presents experimental results comparing the given parallel algorithm with sequential MINPACK code executed on a single processor. These experimental results show that essentially full efficiency is obtained for problems where the row size is sufficiently larger than the number of processors.