Computational Topics in Variational Inequalities and Complementarity Problems

【摘要】约翰霍普金斯大学提出的研究涉及变分不等式和互补性问题领域的三个当代主题。这些主题是：(a)具有平衡约束的数学程序，(b)拟变分不等式，以及(c)微分互补系统。在每个案例中，我们的重点是设计，实施和分析稳健和有效的数值方法来解决所研究的问题。所提出的方法将得到强有力的理论基础的支持，有助于提供对问题的深入理解。将发展的理论和计算算法应用于工程设计、参数识别、经济均衡、电力规划和定价、约束机械系统以及金融工程中的衍生品定价等重要学科问题，也将被仔细研究。总的来说，我们的研究是建立在我们过去在数学规划这个广阔的子领域所取得的成功的基础上的。该项目的主要目标是将这一子领域扩展到一些新的未知应用领域，这些应用领域迫切需要本文所提出的计算研究。

ABSTRACTProposal #0098013Johns Hopkins UniversityThe proposed research is concerned with three contemporary topics in the area of variational inequalities and complementarity problems. These topics are: (a) mathematical programs with equilibrium constraints, (b) quasi-variational inequalities, and (c) differential complementarity systems. In each case, our focus is on the design, implementation, and analysis of robust and efficient numerical methods for solving the problems under study. The proposed methods will be supported by a strong theoretical foundation that serves to provide an in-depth undertanding of the problems. Applications of the developed theory and computational algorithms to important disciplinary problems in engineering design, parameter identification, economic equilibria, electric power planning and pricing, constrained mechanical systems, and derivative pricing in financial engineering will also be carefully investigated. Overall, our research is built on the past success we have had in this vast subarea of mathematical programming. The main goal of the project is to expand this subarea in some new unchartered domains of applications that urgently require the kind of computational research proposed herein.