Mechanical Engineering Building
1513 University Avenue
Madison, WI 53706-1539
Ph: (608) 263-6862
Fax: (608) 262-8454
Industrial and Systems Engineering
My research is in the development of quantitative methods for making the best use of scarce resources, which is part of the broad category of operations research methods. Within that category, I work particularly on nonlinear and stochastic optimization methods for both optimization and equilibrium problems, trying both to develop the underlying theory and to find better numerical methods for solving applied problems. I have developed algorithms for deterministic nonlinear problems, as well as sample-path algorithms for stochastic optimization problems. My recent work has focused especially on the mathematical properties of solutions of variational conditions, considered as functions of the data appearing in those conditions. For these problems I am working on efficient reparametrization methods for problem expression, on implicit-function methods for representing solutions as functions of the data, and on conditions to ensure Lipschitz continuity of solutions. Using these tools I am also developing numerical methods for efficient solution of variational conditions, based on generalized linearization among other techniques.