Frontiers in PDE-constrained optimization. (2018)

• Record Type: Book
• Further Information: Note: Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal, editors.
• Editors: Antil, Harbir; Kouri, Drew P; Lacasse, Martin-D; Ridzal, Denis
• Other Names: Frontiers in PDE-constrained optimization (Workshop)
• Contents: Intro; Foreword; Preface; Contents; Part I PDE-Constrained Optimization: Tutorials; A Brief Introduction to PDE-Constrained Optimization; 1 Introduction; 2 Abstract Optimization Problem; 2.1 Existence; 2.2 Differentiation in Banach Spaces; 2.3 First-Order Necessary Optimality Conditions; 3 Application to PDE-Constrained Optimization Problems; 3.1 Reduced Form: First-Order Necessary Optimality Conditions; 3.2 Lagrangian Formulation; 3.2.1 First-Order Optimality Conditions; 3.2.2 Second-Order Derivatives; 4 Sobolev Spaces; 5 Second-Order Linear Elliptic PDEs; 5.1 Existence and Uniqueness 5.2 Regularity6 Linear Quadratic PDE-Constrained Optimization Problem; 6.1 Problem Formulation; 6.2 Reduced PDECO Problem; 6.3 First-Order Optimality Conditions; 6.4 Lagrange Method; 7 Semilinear Quadratic PDE-Constrained Optimization Problem; 8 Discrete Optimal Control Problem; 8.1 Discrete Linear Quadratic PDE-Constrained Optimization Problem; 8.2 Optimization Problem Without Control Constraints; 8.3 Optimization Problem with Control Constraints; 8.3.1 Cell-Wise Constant Control Discretization; 8.3.2 Cell-Wise Linear Control Discretization; 8.4 Semilinear Equations 9 Conclusion and the Current State of the ArtReferences; Optimization of PDEs with Uncertain Inputs; 1 Introduction; 2 Tensor Product Spaces; 3 Problem Formulation; 3.1 Existence of Minimizers and Optimality Conditions; 3.2 Linear Elliptic Optimal Control; 4 Choosing the Functional R; 4.1 Risk-Averse Optimization; 4.2 Probabilistic Optimization; 4.3 Distributionally Robust Optimization; 5 Methods for Expectation-Based Optimization; 5.1 Stochastic Approximation; 5.2 Sample Average and Quadrature Approximation; 5.3 Progressive Hedging; 6 Numerical Example; 7 Conclusions; References Inexact Trust-Region Methods for PDE-Constrained Optimization1 Introduction; 2 Notation; 3 Problem Formulations; 4 Inexact Trust-Region Methods; 4.1 A Reduced-Space Approach; 4.1.1 Related Work; 4.2 A Full-Space Approach; 4.2.1 Computation of the Quasi-Normal Step; 4.2.2 Solution of the Tangential Subproblem; 4.2.3 Computation of the Tangential Step; 4.2.4 Computation of the Lagrange Multipliers; 4.2.5 Full-Space Trust-Region SQP Algorithm with Inexact Linear System Solves; 4.2.6 Related Work; 5 Application to Risk-Neutral Optimization; 5.1 Sparse-Grid Adaptivity 5.1.1 Computation of Inexact Gradient5.1.2 Computation of Inexact Objective Function Value; 5.2 Iterative Linear System Solves; 6 Numerical Examples; 6.1 Reduced-Space Results with Adaptive Sparse Grids; 6.2 Full-Space Results with Iterative Linear System Solves; 6.3 Reproducibility; 7 Conclusions; References; Numerical Optimization Methods for the Optimal Controlof Elliptic Variational Inequalities; 1 Introduction; 2 Notation, Assumptions, and Preliminary Results; 2.1 Norms, Inner Products, and Convergence; 2.2 Extended Real-Valued Functionals and Convex Analysis
• Publisher Details: New York, NY : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 519.6; Mathematics; Constrained optimization -- Congresses; Differential equations, Partial -- Congresses; Differential equations, partial; Mathematical optimization; Topology; MATHEMATICS / Applied; MATHEMATICS / Probability & Statistics / General; Mathematics -- Applied; Mathematics -- Topology; Applied mathematics; Optimization; Topology; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9781493986361; 1493986368
• Related ISBNs: 9781493986354
• Notes: Note: Online resource; title from PDF title page (SpringerLink, viewed October 17, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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