9303772 Burke This project comprises three areas of study: (1) robust methods in nonlinear programming, including development of algorithms for problems involving infeasibility and lack of regularity; (2) least-squares methods for nonlinear complementarity, and development of globally defined algorithms based on a least-squares methodology, and (3) eigenvalue optimization and eigenvalue problems. This research can significantly expand the traditional domain of applications for nonlinear programming methods. For example, techniques for infeasible nonlinear programs can be applied to guide a system through a catastrophic event; e.g., the maintenance of power flow in a power grid that can no longer meet demand due to a downed transmission line or a damaged switching station. Global strategies in nonlinear complementarity may permit the solution of discrete infinite dimensional nonlinear variational inequalities; e.g., the variational inequalities found in liquid crystal simulation. The research into variational principles in eigenvalue optimization has wide application in the optimal design of stable structures having nonlinear dynamics. ***
