Rb. Schnabel, A VIEW OF THE LIMITATIONS, OPPORTUNITIES, AND CHALLENGES IN PARALLEL NONLINEAR OPTIMIZATION, Parallel computing, 21(6), 1995, pp. 875-905
Citations number
44
Categorie Soggetti
Computer Sciences","Computer Science Theory & Methods
The availability and power of parallel and distributed computers is ha
ving a significant impact on how expensive problems are solved in all
areas of numerical computation, and is likely to have an even larger i
mpact in the future. This paper presents a view of how the considerati
on of parallelism is affecting, and is likely to affect, one important
field within numerical computation, the field of nonlinear optimizati
on. It does not attempt to survey the research that has been done in p
arallel nonlinear optimization. Rather it presents a set of examples,
drawn mainly from our own research, that illustrate many of the limita
tions, opportunities, and challenges inherent in incorporating paralle
lism into the field of nonlinear optimization. These examples include
parallel methods for unconstrained optimization problems with a small
to moderate number of variables, parallel methods for large block bord
ered systems of nonlinear equations, and parallel methods for small-sc
ale and large-scale global optimization problems. Our overall conclusi
ons are mixed. For most generic optimization problems with a small to
moderate number of variables, the consideration of parallelism does no
t appear to be leading to major algorithmic innovations. For many clas
ses of large-scale problems, however, the consideration of parallelism
appears to be creating opportunities for the development of interesti
ng new methods that may be advantageous on parallel and sometimes even
on sequential computers. In addition, a number of large-scale paralle
l optimization algorithms exhibit irregular, coarse-grain structure, w
hich leads to interesting computer science challenges in areas such as
dynamic scheduling and load-balancing.