AN EVALUATION OF NONLINEAR OPTIMIZATION CODES ON SUPERCOMPUTERS

Abstract

The introduction of vector and parallel supercomputers in the last decade generates a significant impact on large-scale scientific computing. Computational optimization is one important area that is rapidly evolving to benefit from novel computer architectures. In this paper, we restrict our discussions to numerical methods for nonlinear unconstrained optimization. Many important applications fall into this category, and these methods often serve as the basis for other iterative procedures that are generally used in solving nonlinear programming problems. There exists a large array of methods for solving nonlinear unconstrained optimization problems Various implementations of many of these methods can be obtained from the open literature including journals and textbooks. Only a selective number of those techniques have been shown to be most robust and efficient; some of them are currently distributed as commercial software libraries. Testing and comparing these optimization codes is very important since it provides some prior measure of efficiency and robustness of the codes and will show the suitability of a code for solving a particular application problem at hand. Although many numerical evaluations of unconstrained optimization methods have been published, most of them were geared towards relatively small dimensional problems, and very few of them were based on implementations available in public software libraries. Comparison of specific implementations is necessary since the performance of a particular algorithm can vary widely from implementation to implementation. Technical details of the programming and slight changes in the line search techniques, restart criterion, updating formulas, and the like could make a significant difference in the performance of an algorithm. In this paper, we compare the performances of several unconstrained optimization codes available in the leading numerical libraries. These software libraries receive widespread usage in the scientific community worldwide. In particular, we are interested in solving problems for which the number of variables n is of medium to large size, say up to 10,000 variables. Numerical results are obtained using an NEC SX-IA supercomputer.