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.
Inhaltsverzeichnis
I Introduction. - Large-Scale PDE-Constrained Optimization: An Introduction. - II Large-Scale CFD Applications. - Nonlinear Elimination in Aerodynamic Analysis and Design Optimization. - Optimization of Large-Scale Reacting Flows using MPSalsa and Sequential Quadratic Programming. - III Multifidelity Models and Inexactness. - First-Order Approximation and Model Management in Optimization. - Multifidelity Global Optimization Using DIRECT. - Inexactness Issues in the Lagrange-Newton-Krylov-Schur Method for PDE-constrained Optimization. - IV Sensitivities for PDE-based Optimization. - Solution Adapted Mesh Refinement and Sensitivity Analysis for Parabolic Partial Differential Equation Systems. - Challenges and Opportunities in Using Automatic Differentiation with Object-Oriented Toolkits for Scientific Computing. - Piggyback Differentiation and Optimization. - V NLP Algorithms and Inequality Constraints. - Assessing the Potential of Interior Methods for Nonlinear Optimization. - An Interior-Point Algorithm for Large Scale Optimization. - SQP SAND Strategies that Link to Existing Modeling Systems. - Interior Methods For a Class of Elliptic Variational Inequalities. - Hierarchical Control of a Linear Diffusion Equation. - VI Time-Dependent Problems. - A Sequential Quadratic Programming Method for Nonlinear Model Predictive Control. - Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition. - Adaptive Simulation, the Adjoint State Method, and Optimization. - VII Frameworks for PDE-Constrained Optimization. - 18 The SIERRA Framework for Developing Advanced Parallel Mechanics Applications. - rSQP++: An Object-Oriented Framework for Successive Quadratic Programming. - Sundance Rapid Prototyping Tool for Parallel PDE Optimization. - Color Plates.
