Multilevel Optimization Methods for Engineering Design and PDE-Constrained OptimizationStephen G. Nash
George Mason University, Systems Engineering and Operations Research Department
Tuesday, September 8, 2009 15:00-16:00,
Many large nonlinear optimization problems are based upon a hierarchy of models, corresponding to levels of discretization or detail in the problem. Optimization-based multilevel methods - that is, multilevel methods based on solving coarser approximations of an optimization problem - are designed to solve such multilevel problems efficiently by taking explicit advantage of the hierarchy of models. The methods are generalizations of more traditional multigrid methods for solving partial differential equations. However, the optimization approach admits a richer class of models and has better guarantees of convergence. The optimization-based multilivel methods also generalize model-management approaches for solving engineering design problems.
These multilevel methods are a powerful tool, and can dramatically out-perform traditional optimization algorithms. However, they are not general-purpose methods. I will describe techniques whereby a particular multilevel method can assess the properties of the optimization problem, with the goal of automatically determining whether the optimization problem is well suited for the multilevel algorithm. I will also show that the diagnostic tests are sufficient to measure the properties of the optimization problem that are relevant to the performance of the multilevel method.
Speaker Bio: Stephen Nash received a B.Sc. (Honours) degree in mathematics in 1977 from the University of Alberta, Canada; and a Ph.D. in computer science in 1982 from Stanford University. He is a Professor of Systems Engineering and Operations Research in the School of Information Technology and Engineering. Prior to coming to George Mason University, he taught at The Johns Hopkins University. From 2005-2008 he served as a program officer at the National Science Foundation. He has also had professional associations with the National Institute of Standards and Technology, and the Argonne National Laboratory. His research activities are centered in scientific computing, especially nonlinear optimization. He has been a member of the editorial boards of Operations Research, Mathematical Methods of Operations Research, Computers in Science & Engineering, the SIAM Journal on Scientific Computing, and the Journal of the American Statistical Association.
Contact: R. F. Boisvert
Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.