Ebook: 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.

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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.

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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.

Content:
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

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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.

Content:
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
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