===firstname:
Elizabeth
===firstname3:
Martin
===affil6:

===lastname3:
Grepl
===email:
elizqian@mit.edu
===keyword_other2:

===lastname6:

===affil5:
MIT
===lastname4:
Veroy
===lastname7:

===affil7:

===postal:
77 Massachusetts Avenue
Room 37-312
Cambridge, MA 02139
===ABSTRACT:
Parameter optimization problems constrained by partial differential equations (PDEs) appear in many science and engineering applications. Solving these optimization problems may require a prohibitively large number of computationally expensive PDE solves, especially if there are many variable parameters. It is therefore advantageous to replace expensive high-dimensional PDE solvers (e.g.\ finite element) with lower-dimension surrogate models. In this paper, we use the reduced basis (RB) model reduction method in conjunction with a trust region optimization framework to accelerate PDE-constrained parameter optimization. New \emph{a posteriori }error bounds on the RB cost and cost gradient for quadratic cost functionals are presented, and used to guarantee convergence to the optimum of the high-fidelity model. The proposed certified RB trust region approach thus requires only a minimal number of high-order solves, used to update the RB model if the approximation is no longer sufficiently accurate. We consider problems governed by elliptic PDEs and present numerical results for a thermal fin model problem with six parameters. 
===affil3:
RWTH Aachen University, Germany
===title:
A Certified Reduced Basis Approach to PDE-constrained Parameter Optimization
with Quadratic Cost Functionals
===affil2:
RWTH Aachen University, Germany
===lastname2:
Qian
===firstname4:
Karen
===keyword1:
Optimization of Complex Problems/Systems
===workshop:
no
===lastname:
Qian
===firstname5:
Karen
===keyword2:
Surrogate modeling/model reduction
===otherauths:

===affil4:
RWTH Aachen University, Germany
===competition:
yes
===firstname7:

===firstname6:

===keyword_other1:

===lastname5:
Willcox
===affilother:

===firstname2:
Elizabeth