Oral Defense of Doctoral Dissertation – Computational Sciences and Informatics – Function Space Nonlinear Rescaling Methods For Elliptic Control Problems With Point-Wise State And Control Constraints – Joel M. Mejeur

Notice and Invitation
Oral Defense of Doctoral Dissertation
Doctor of Philosophy in Computational Sciences and Informatics
Department of Computational and Data Sciences
College of Science
George Mason University

Joel M. Mejeur
Bachelor of Science, Taylor University, 2000
Master of Science, University of Tennessee, 2002
Master of Engineering-Physics, University of Virginia, 2008

FUNCTION SPACE NONLINEAR RESCALING METHODS FOR ELLIPTIC
CONTROL PROBLEMS WITH POINT-WISE STATE AND CONTROL CONSTRAINTS

Thursday, November 30, 10:30 a.m.
Exploratory Hall, Room 3301

All are invited to attend.

Committee
Igor Griva, Dissertation Director
Padmanabhan Seshaiyer
Chi Yang
Fernando Camelli

State inequality constraints in PDE Constrained Optimization (PDECO) arise in many areas of science and engineering. Unfortunately these constraints, and the resulting Lagrange multipliers, are known to negatively influence the behavior of many existing optimization methods. In this work Nonlinear Rescaling based methods are used for the state and control constraints. In particular, a Nonlinear Rescaling-Primal Dual Augmented Lagrangian method is analyzed and proven to have linear convergence for state and control constrained problems. In addition, a Primal Dual Nonlinear

Rescaling Augmented Lagrangian method is analyzed for control constraints and shown to have superlinear convergence properties. In each of the derived methods the Finite Element Method will be used to construct and solve the discretized version of the inner iteration.

A copy of Joel’s dissertation is available for examination from Karen Underwood, Department of Computational and Data Sciences, 373 Research Hall. The dissertation is available to read only within the Department and cannot be taken out of the Department or copied.