Computational Topics in Variational Inequalities and Complementarity Problems

约翰·霍普金斯大学提议的研究涉及变分不等和互补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规划，(B)拟变分不等式，和(C)微分互补系统。在每一种情况下，我们的重点都是设计、实现和分析稳健而有效的数值方法来解决所研究的问题。提出的方法将得到坚实的理论基础的支持，这有助于对问题的深入了解。还将仔细研究所开发的理论和计算算法在工程设计、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上的应用。总体而言，我们的研究是建立在我们在数学规划这一广阔的子领域取得的过去成功的基础上的。该项目的主要目标是在一些新的未知应用领域扩大这一分区，这些领域迫切需要这里提出的那种计算研究。

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.