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。例子包括像拥挤的交通网络、电信和计算机系统以及资源分配网络这样的大型系统。由于此类应用需要及时解决，因此网络算法必须设计为高效计算，从而利用任何特殊的问题结构和高性能计算机体系结构。在这个项目中，几个串行和并行的平衡算法将开发纯和广义的非线性网络流问题，有和没有容量。对于固定需求问题和弹性需求问题，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对计算机存储的要求。首先推导了二次型网络的平衡算法，然后推导了高度非线性网络的平衡算法，并建立了收敛条件。然后将定义网络拓扑结构以构建专门的算法。所有算法都将在不同的架构上进行计算测试，使用来自各种应用程序的真实世界数据，以实证地展示它们的性能。Nagurney博士将在1989年春季为高年级本科生和研究生开设一门关于网络均衡的课程从竞争均衡问题和变分不等式的角度进行教授。她将针对非线性网络流问题的平衡算法的研究进行一系列的讲座。此外，纳格尼博士将组织一个杰出的系列讲座，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。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。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.