Nonlinear optimization and parallel computing

The new computational technologies are having a very strong influence on numerical optimization, in several different ways. Many researchers have been stimulated by the need to either conform the existing numerical techniques to the new parallel architectures or to devise completely new parallel solution approaches. A mini-symposium on Parallel Computing in Nonlinear Optimization was held in Naples, Italy, September 2001, during the International Conference ParCo2001, in order to bring together researchers active in this field and to discuss and share their findings. Some of the papers presented during the mini-symposium, as well as additional contributions from other researchers are collected in this special issue. Clearly, two different trends, well representative for most of the current research activities, can be identified. Firstly, there is an attempt to encapsulate parallel linear algebra software and algorithms into optimization codes, particularly codes implementing interior point strategies for which the linear algebra issues are very critical, and secondly, there is an effort to devise new parallel solution strategies in global optimization, either for specific or general purpose problems, motivated by the large size and the combinatorial nature of them. In the present paper we review the literature on these trends and classify the contributed papers within this framework.