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Research SummaryThe major thrust of my research is in providing tools to operations researchers, economists and engineers that help them to understand and solve their models. Problem analysis routines, data manipulations and solution visualization procedures are being developed to aid both solver routines and model developers. I am developing software (EMP) that converts MOPECs and generalized Nash Equilibiria into complementarity problems without human interaction, using automatic differentiation techniques. Current work is also investigating how to easily formulate and solve practical optimization problems using structure exploiting methods for problem decomposition.I am interested in using optimization in applications ranging from energy, environmental policy and video-on-demand to radiation therapy. I also continue to investigate robust methods for solving large-scale variational inequality and nonlinear programming problems with applications to problems in economics and engineering. Algorithmic work related to complementarity solvers is attempting to solve large scale models in a robust and numerically stable fashion. To this end, we continue to develop new algorithms and implementations, along with testing beds and techniques for succinctly modeling both complementarity problems, mathematical programs with equilibrium constraints, and general but structured equilibrium problems. Optimization within Gamma Knife Radiosurgery
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