2002 г., Том 7, Спец. выпуск, с.27-62

In these years, we note a growing interest in theoretical foundations and methods which discrete optimization and continuous optimization have in common. There is hope that both fields may learn from each other, and that there will be such a unification that tradition, character and importance of each field remain preserved ( Dress [65], Gritzmann [88]). This survey article is based on the work Weber [289] on the large class of generalized semi-infinite (continuous) optimization problems, generically including optimal control theory. We indicate discrete-combinatorial aspects of an iteration procedure based on local linearization. Furthermore, we explain combinatorial relations between graphs and nonlinear optimization problems, topological properties of graphs and networks, optimal control applications of networks, symmetric multi-processing systems, random graphs and their Morse theoretical aspects, Newton flows and their discrete features. Throughout the article we pay attention to structural frontiers, and we motivate future research.