Speaker: Stephen Nash, George Mason University

Title: Multilevel Optimization Methods for Engineering Design and PDE-Constrained Optimization

Abstract: 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.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491