Serial and Parallel Algorithms for Large-Scale Nonlinear Network Flow Problems (Engineering)

工程中的许多问题都可以用非线性网络流问题来建模和研究。例如，拥堵的交通网络、电信和计算机系统以及资源分配网络等大规模系统。由于此类应用需要及时解决，因此网络算法必须设计成高效的计算，从而利用任何特殊的问题结构和高性能的计算机体系结构。在这个项目中，将针对纯和广义的有能力和无能力的非线性网络流问题开发几种串并平衡算法。对于固定需求和弹性需求问题，都将使用问题的节点链接公式，而不是路径，以大大减少此类算法的计算机存储需求。首先推导出二次网络的均衡算法，然后对高度非线性的网络推导出均衡算法，并建立收敛条件。然后将定义网络拓扑以构建专门的算法。所有算法都将使用来自各种应用程序的真实数据在不同的体系结构上进行计算测试，以经验地演示它们的性能。Nagurney博士将于1989年春季为高水平本科生和研究生开发并讲授一门关于网络均衡的课程，该课程将从竞争均衡问题和变分不等的角度进行讲授。她将为教师和学生举办一系列讲座，介绍她对非线性网络流量问题的平衡算法的研究。此外，纳格尼博士还将组织一系列杰出的讲座，邀请资深女性学者到麻省理工学院讲述她们作为女性研究人员的经历。该项目进一步推动了VPW计划的目标，即：(1)为妇女提供机会，在NSF资助的工程和科学学科中发展她们的职业生涯；(2)通过提高受雇于工业、政府和学术机构的女科学家和工程师的知名度，鼓励妇女追求科学和工程事业。通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。

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.