Computational Topics in Variational Inequalities and Complementarity Problems

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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.