Many problems in engineering can be modeled and studied as nonlinear network flow problems. Examples include such large- scale systems as congested transportation networks, telecommuni- cation and computer systems, and resource distribution networks. Since such applications require timely solution, network algorithms must be designed for efficient computation and, hence, take advantage of any special problem structure and high- performance computer architectures. In this project, several serial and parallel equilibration algorithms will be developed for pure and generalized nonlinear network flow problems, with and without capacities. The node-link formulation of the problems, rather than the path, will be used for both fixed and elastic demand problems to substantially reduce the computer storage requirements of such algorithms. First, equilibration algorithms will be derived for quadratic networks, and then for more highly nonlinear networks, and convergence conditions established. Network topologies will then be defined to construct specialized algorithms. All algorithms will be computationally tested on different architectures using real- world data arising from a variety of applications, to demonstrate empirically their performance. Dr. Nagurney will develop and teach a course for upper-level undergraduates and graduate students on network equilibrium taught from the standpoint of competitive equilibrium problems and variational inequalities, in the spring 1989. She will conduct a series of lectures to faculty and students about her research on equilibrium algorithms for nonlinear network flow problems. In addition, Dr. Nagurney will organize a distinguished lecture series in which senior female scholars will be invited to M.I.T. to relate their experiences as female researchers. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.
