Large-Scale PDE-Constrained Optimization

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. Front Matter....Pages I-VI Front Matter....Pages 1-1 Large-Scale PDE-Constrained Optimization: An Introduction....Pages 3-13 Front Matter....Pages 15-15 Nonlinear Elimination in Aerodynamic Analysis and Design Optimization....Pages 17-43 Optimization of Large-Scale Reacting Flows using MPSalsa and Sequential Quadratic Programming....Pages 45-59 Front Matter....Pages 61-61 First-Order Approximation and Model Management in Optimization....Pages 63-79 Multifidelity Global Optimization Using DIRECT....Pages 80-92 Inexactness Issues in the Lagrange-Newton-Krylov-Schur Method for PDE-constrained Optimization....Pages 93-114 Front Matter....Pages 115-115 Solution Adapted Mesh Refinement and Sensitivity Analysis for Parabolic Partial Differential Equation Systems....Pages 117-132 Challenges and Opportunities in Using Automatic Differentiation with Object-Oriented Toolkits for Scientific Computing....Pages 133-147 Piggyback Differentiation and Optimization....Pages 148-164 Front Matter....Pages 165-165 Assessing the Potential of Interior Methods for Nonlinear Optimization....Pages 167-183 An Interior-Point Algorithm for Large Scale Optimization....Pages 184-198 SQP SAND Strategies that Link to Existing Modeling Systems....Pages 199-217 Interior Methods For a Class of Elliptic Variational Inequalities....Pages 218-235 Hierarchical Control of a Linear Diffusion Equation....Pages 236-249 Front Matter....Pages 251-251 A Sequential Quadratic Programming Method for Nonlinear Model Predictive Control....Pages 253-267 Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition....Pages 268-280 Adaptive Simulation, the Adjoint State Method, and Optimization....Pages 281-297 Front Matter....Pages 299-299 The SIERRA Framework for Developing Advanced Parallel Mechanics Applications....Pages 301-315 rSQP++ : An Object-Oriented Framework for Successive Quadratic Programming....Pages 316-330 Sundance Rapid Prototyping Tool for Parallel PDE Optimization....Pages 331-341 Back Matter....Pages 343-355