Coverart for item
The Resource Frontiers in PDE-constrained optimization, Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal, editors

Frontiers in PDE-constrained optimization, Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal, editors

Label
Frontiers in PDE-constrained optimization
Title
Frontiers in PDE-constrained optimization
Statement of responsibility
Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal, editors
Contributor
Editor
Subject
Genre
Language
eng
Member of
Cataloging source
N$T
Dewey number
519.6
Index
no index present
LC call number
QA402.5
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
2016
http://library.link/vocab/relatedWorkOrContributorName
  • Antil, Harbir
  • Kouri, Drew P.
  • Lacasse, Martin-D.
  • Ridzal, Denis
  • Workshop "Frontiers in PDE-Constrained Optimization"
Series statement
The IMA volumes in mathematics and its applications,
Series volume
volume 163
http://library.link/vocab/subjectName
  • Constrained optimization
  • Differential equations, Partial
Label
Frontiers in PDE-constrained optimization, Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal, editors
Instantiates
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781493986361
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
http://library.link/vocab/ext/overdrive/overdriveId
com.springer.onix.9781493986361
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1057018391
  • (OCoLC)1057018391
Label
Frontiers in PDE-constrained optimization, Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal, editors
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781493986361
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
http://library.link/vocab/ext/overdrive/overdriveId
com.springer.onix.9781493986361
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1057018391
  • (OCoLC)1057018391

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