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Abstract:
A new approach is presented to the problem of finding a global (i.e. absolute) minimizer of a function of several real variables, and some of its mathematical properties are investigated. The approach is based on the idea of following the solution trajectories of a stochastic differential equation inspired by statistical mechanics. This document also describes a complete algorithm (SIGMA) based on the above approach, which looks for a point of global minimum by monitoring the values of the function to be minimized along a number of simultaneously-evolving trajectories generated by a new (stochastic) scheme for the numerical integration of the stochastic differential equation. Finally described is the software package SIGMA which implements the above algorithm in a portable subset of the A.N.S. FORTRAN IV language, a number of carefully selected test problems designed for testing the software for global optimization, and the results of testing SIGMA on the above problems, and on a problem of theoretical chemistry. The main conclusion is that the performance of SIGMA is very good, even on some very hard problems. Additional keywords: Numerical Analysis; Mathematical software; Algorithm analysis, certification and testing. (Author)
| Description: |
Final technical rept. Dec 81-Dec 84 |
| Pages: |
282 |
| Report Date: |
DEC 84 |
| Contract Number: |
DAJA37-81-C-0740 |
| Report Number: |
A645751 |
Report Unavailable |
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