Large-Scale Pde-Constrained Optimization

by Biegler, Lorenz T.; Ghattas, Omar; Heinkenschloss, Matthias; Van Bloemen Waanders, Bart; Bloemen Waamders, Bart Van

• ISBN13: 9783540050452
• ISBN10: 3540050450
• Format: Paperback
• Copyright: 2003-10-01
• Publisher: Springer Verlag

Summary

Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Table of Contents

I Introduction
Large-Scale PDE-Constrained Optimization: An Introduction	3	(14)
Lorenz T. Biegler, Omar Ghattas, Matthias Heinkenschloss, Bart van Bloemen Waanders
II Large-Scale CFD Applications
Nonlinear Elimination in Aerodynamic Analysis and Design Optimization	17	(28)
D.P. Young, W.P. Huffman, R.G. Melvin, C.L. Hilmes, F.T. Johnson
Optimization of Large-Scale Reacting Flows using MPSalsa and Sequential Quadratic Programming	45	(18)
A.G. Salinger, R.P. Pawlowski, J.N. Shadid, B. van Bloemen Waanders, R. Bartlett, G.C. Itle, L. Biegler
III Multifidelity Models and Inexactness
First-Order Approximation and Model Management in Optimization	63	(17)
Natalia M. Alexandrov, Robert Michael Lewis
Multifidelity Global Optimization Using DIRECT	80	(13)
Steven E. Cox, Raphael T. Haftka
Inexactness Issues in the Lagrange-Newton-Krylov-Schur Method for PDE-constrained Optimization	93	(24)
George Biros, Omar Ghattas
IV Sensitivities for PDE-based Optimization
Solution Adapted Mesh Refinement and Sensitivity Analysis for Parabolic Partial Differential Equation Systems	117	(16)
Shengtai Li, Linda R. Petzold, James M. Hyman
Challenges and Opportunities in Using Automatic Differentiation with Object-Oriented Toolkits for Scientific Computing	133	(15)
Paul Hovland, Steven Lee, Lois Mclnnes, Boyang Norris, Barry Smith
Piggyback Differentiation and Optimization	148	(19)
Andreas Griewank, Christèle Faure
V NLP Algorithms and Inequality Constraints
Assessing the Potential of Interior Methods for Nonlinear Optimization	167	(17)
José Luis Morales, Jorge Nocedal, Richard A. Waltz, Guanghui Lin, Jean-Pierre Goux
An Interior-Point Algorithm for Large Scale Optimization	184	(15)
John T. Betts, Samuel K. Eldersveld, Paul D. Frank, John G. Lewis
SQP SAND Strategies that Link to Existing Modeling Systems	199	(19)
Lorenz T. Biegler and Andreas Wächter
Interior Methods For a Class of Elliptic Variational Inequalities	218	(18)
Randolph E. Bank, Philip E. Gill, Roummel F. Marcia
Hierarchical Control of a Linear Diffusion Equation	236	(17)
Anthony J. Kearsley, Jon W. Tolle, Paul T. Boggs
VI Time-Dependent Problems
A Sequential Quadratic Programming Method for Nonlinear Model Predictive Control	253	(15)
Kenneth R. Muske, James W. Howse
Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition	268	(13)
Marco Fahl, Ekkehard W. Sachs
Adaptive Simulation, the Adjoint State Method, and Optimization	281	(20)
Mark S. Gockenbach, William W. Symes
VII Frameworks for PDE-Constrained Optimization
The SIERRA Framework for Developing Advanced Parallel Mechanics Applications	301	(15)
James R. Stewart, H. Carter Edwards
rSQP++ : An Object-Oriented Framework for Successive Quadratic Programming	316	(15)
Roscoe A. Bartlett, Lorenz T. Biegler
Sundance Rapid Prototyping Tool for Parallel PDE Optimization	331	(12)
Kevin R. Long
Color Plates	343