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[null,"1.","Record Nr.",null,"UNISA996466419803316"]
[null,null,"Titolo",null,"Non-smooth and complementarity-based distributed parameter systems : simulation and hierarchical optimization / / edited by Michael Hintermüller, [and three others]"]
[null,null,"Pubbl/distr/stampa",null,"Cham, Switzerland : , : Springer, , [2022]"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"3-030-79393-1"]
[null,null,"Descrizione fisica",null,"1 online resource (518 pages)"]
[null,null,"Collana",null,"International Series of Numerical Mathematics ; ; v.172"]
[null,null,"Disciplina",null,"003.78"]
[null,null,"Soggetti",null,"Distributed parameter systems"]
[{"$nulls":4},"Teoria de control"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Contents -- Error Bounds for Discretized Optimal Transport and Its Reliable Efficient Numerical Solution -- 1 Introduction -- 2 Discretized Optimal Transport -- 2.1 General Formulation -- 2.2 Discretization -- 2.3 Optimality Conditions -- 2.4 Sparsity -- 3 Error Analysis -- 4 Active-Set Strategy -- 5 Numerical Experiments -- 5.1 Problem Specifications -- 5.2 Complexity Considerations -- 5.3 Experimental Convergence Rates -- References -- Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems -- 1 Introduction -- 1.1 Cerebral Palsy -- 1.2 Modeling Approach -- 2 Modeling the Human Body -- 2.1 Rigid Multi-Body Systems -- 2.2 Detailed Submodules -- 2.2.1 Foot Modeling and Ground Contact -- 2.2.2 Muscle Modeling -- 2.3 Biomechanical Model for p03-cp Patients -- 3 Modeling the Human Gait -- 3.1 A Multi-Phase Optimal Control Approach -- 3.2 A Mixed-Integer Optimal Control Approach -- 4 Two Bilevel Problems for Diagnosis and Therapy Design of Cerebral Palsy -- 4.1 An Inverse Optimal Control Problem for Diagnosis of Cerebral Palsy -- 4.2 A Robustified Optimal Control Problem for Therapy Design of Cerebral Palsy -- 5 Conclusions and Outlook -- References -- ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation -- 1 Introduction -- 2 A Continuation Method for MOPs with Inexact Objective Gradients -- 2.1 Multiobjective Optimization -- "]
[{"$nulls":4},"2.2 Continuation Method with Exact Gradients -- 2.3 Continuation Method with Inexact Gradients -- 2.3.1 Strategy 1 -- 2.3.2 Strategy 2 -- 2.4 Globalization Approach -- 3 Multiobjective Optimization of an Elliptic PDE Using the RB Method -- 3.1 Multiobjective Optimization of an Elliptic PDE -- 3.2 The Reduced Basis Method -- 3.3 Error Estimation for the Gradients -- 4 Numerical Results."]
[{"$nulls":4},"4.1 Generation of the Reduced Basis -- 4.2 Application of the Continuation Methods to an MPOP -- 5 Conclusion and Outlook -- Appendix A: Proof of Theorem 2.10 -- References -- Analysis and Solution Methods for Bilevel Optimal Control Problems -- 1 Introduction -- 2 Two Example Problems -- 3 Optimality Conditions -- 3.1 Definition of Optimality Systems for (IOCf) -- 3.2 Regularization Approach -- 3.2.1 Assumptions and Properties of the Lower Level Problem -- 3.2.2 C-Stationarity for Local Minimizers -- 3.3 Relaxation Approach -- 3.3.1 The Optimal Value Reformulation and Its Relaxation -- 3.3.2 C-Stationarity for Local Minimizers -- 3.4 Variational Analysis Approach and Mordukhovich-Stationarity -- 3.5 Comments on Biactivity and S-Stationarity -- 4 Numerical Solution -- 4.1 Global Solution Algorithm for ([eq:upperlevel]IOCf2) -- 4.2 Numerical Example -- 5 Future Perspectives -- References -- A Calculus for Non-smooth Shape Optimization with Applications to Geometric Inverse Problems -- 1 Introduction -- 2 Image Reconstruction on Surfaces -- 2.1 Functions of Bounded Variation on Surfaces -- 2.2 Dual Representation -- 2.3 Implementation Details and Numerical Results -- 2.4 Discrete Total Variation -- 3 Shape Optimization Using Total Variation of the Normal Vector Field -- 3.1 Total Variation of Normal -- 3.2 Mesh Denoising -- 3.3 Inverse Problem -- 4 Conclusion and Outlook -- References -- Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control -- 1 Introduction -- 2 Rate-Independent Systems and Solution Concepts -- 3 Discretization Schemes for Rate-Independent Systems and Their Convergence -- 3.1 The Semilinear Setting -- 3.2 Discretization Schemes, Abstract Semilinear Setting -- 3.3 A Priori Estimates, Abstract Semilinear Setting -- 3.4 Finite-Element Discretization and Numerical Realization."]
[{"$nulls":4},"4 Optimal Control of Rate-Independent Systems -- 5 Optimal Control of Thermo-Viscoplasticity -- References -- Generalized Nash Equilibrium Problems with Partial Differential Operators: Theory, Algorithms, and Risk Aversion -- 1 Introduction -- 2 Nash Games Involving Nonlinear Operator Equations -- 2.1 On the Convexity of Optimal Control Problems Involving Nonlinear Operator Equations -- 3 Nash Games Using Penalization Techniques -- 3.1 -Convergence -- 4 PDE-Constrained GNEPs Under Uncertainty -- 4.1 Motivation -- 4.2 Additional Notation and Preliminary Results -- 4.3 Risk-Averse PDE-Constrained Optimization: Theory -- 4.4 A Risk-Averse PDE-Constrained Nash Equilibrium Problem -- 4.5 Risk-Averse PDE-Constrained Decision Problems: Smooth Approximation -- 4.6 Risk-Averse PDE-Constrained Optimization: Solution Methods -- 5 Outlook -- References -- Stability and Sensitivity Analysis for Quasi-Variational Inequalities -- 1 Introduction -- 2 QVIs: Mathematical Setting and Existence -- 2.1 Existence of Solutions: Order Approach -- 2.2 Existence of Solutions: Iteration Approach -- 2.3 Miscellaneous: A Pitfall -- 3 Sensitivities -- 3.1 Stability for Minimal and Maximal Solution Maps -- 3.2 Directional Differentiability -- 3.3 Parabolic QVIs -- 3.4 Application to Thermoforming -- 3.4.1 The Model -- 3.4.2 Properties and Existence for the System -- 3.4.3 Numerical Implementation Details -- 3.4.4 Numerical Results -- 4 Control of QVIs -- 5 Outlook -- References -- Simulation and Control of a Nonsmooth Cahn-Hilliard Navier-Stokes System with Variable Fluid Densities -- 1 "]
[{"$nulls":4},"Introduction -- 2 Problem Setting -- 3 Optimal Control of the Semi-Discrete CHNS System -- 3.1 The Semi-Discrete CHNS System and the Optimal Control Problem -- 3.2 Existence of Feasible and Globally Optimal Points -- 3.3 E-Almost C-Stationary Points -- 3.4 Strong Stationarity."]
[{"$nulls":4},"3.5 Adaptive Mesh Refinement -- 3.6 Penalization Algorithm -- 3.7 Bundle-Free Implicit Programming Approach -- 4 Model Order Reduction with Proper Orthogonal Decomposition -- 4.1 POD in Hilbert Spaces with Space-Adapted Snapshots -- 4.2 POD Reduced-Order Modeling for the Cahn-Hilliard System -- 4.3 Numerical Example of POD-MOR for the Cahn-Hilliard System -- 4.4 Stable POD Reduced-Order Modeling for Navier-Stokes with Space-Adapted Snapshots -- 5 Outlook -- References -- Safeguarded Augmented Lagrangian Methods in Banach Spaces -- 1 Introduction -- 2 Background Material -- 2.1 Cones -- 2.2 Convex Functions and Concave Operators -- 2.3 Pseudomonotone Operators -- 2.4 KKT-Type Conditions -- 3 Motivation and Statement of the Algorithm -- 3.1 The Original Method of Multipliers -- 3.2 Inequality Constraints and Slack Variables -- 3.3 The Algorithm -- 4 Global Convergence Theory -- 4.1 Existence of Penalized Solutions -- 4.2 Convergence to Global Minimizers -- 4.3 Stationarity of Limit Points -- 5 Local Convergence -- 5.1 Existence of Local Minima und Strong Convergence -- 5.2 Rate of Convergence -- 6 Numerical Results -- 6.1 State-Constrained Optimal Control Problems -- 6.2 Bratu's Obstacle Problem -- 6.3 C-Minimization -- 7 Final Remarks -- References -- Decomposition and Approximation for PDE-Constrained Mixed-Integer Optimal Control -- 1 Introduction -- 1.1 Outline of the Remaining Sections -- 1.2 Notation -- 2 Approximation Arguments for the CIA Decomposition -- 2.1 Properties of Rounding Meshes and Algorithms -- 2.2 Weak Control Approximation -- 2.3 State Vector Approximation -- 2.4 Optimality and Feasibility in the Absence of Mixed Constraints -- 2.5 Optimality and Feasibility in the Presence of Mixed Constraints -- 3 Approximation Quality of Roundings -- 3.1 Sum-up Rounding Algorithms -- 3.2 Combinatorial Integral Approximation Problems."]
[{"$nulls":4},"4 Solving the CIA Problem -- 5 Illustration of the Multidimensional Control Approximation -- 5.1 Test Problem -- 5.2 Mesh Structure and Sierpinski Curve -- 5.3 Numerical Results Obtained with the CIA Decomposition -- 6 Conclusion -- References -- Strong Stationarity for Optimal Control of Variational Inequalities of the Second Kind -- 1 Introduction -- 2 Strong Stationarity in an Abstract Framework -- 3 Application to Concrete Settings -- 3.1 The Obstacle Problem -- 3.2 Static Elastoplasticity -- 3.3 The Lasso Problem in Sobolev Spaces -- 3.4 Non-Newtonian Fluids: The Mosolov Problem -- 4 Conclusion -- Appendix A: Auxiliary Results -- References -- Optimizing Fracture Propagation Using a Phase-Field Approach -- 1 Introduction -- 2 Problem Setting -- 2.1 Model Problem, Notation, and Assumptions -- 2.2 The Phase-Field Equation -- 3 The Limiting First-Order Necessary Conditions -- 4 An SQP Method for (NLPγ) -- 4.1 The SQP Algorithm -- 4.2 First-Order Optimality Conditions for (QPγ) and Its Limit -- 4.3 Approximation of (QPγ) by Finite Elements -- 5 An SQP Method for (NLPVI) -- 5.1 SQP Algorithm for (NLPVI) -- 5.2 Convergence of FE Approximation to (QPVI) -- References -- Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain -- 1 Introduction -- 2 Contact Problems in Hyperelasticity -- 3 Optimal Control of Nonlinear Elastic Contact Problems -- 4 Numerical Optimization Algorithms -- 4.1 An Affine Covariant Composite Step Method -- 4.2 Computation of Steps by Iterative Solvers -- 4.3 Inexact Constraint Preconditioning -- 4.4 Accuracy Matching -- 4.5 Choice of Functional "]
[{"$nulls":4},"Analytic Framework -- 4.6 Non-convexity of Objective and Energy -- 4.7 Non-convexity of the Energy -- 4.8 Path Following -- 5 Conclusion and Outlook -- References -- Algorithms Based on Abs-Linearization for Non-smooth Optimization with PDE Constraints."]
[{"$nulls":4},"1 Motivation and Introduction."]
[null,"2.","Record Nr.",null,"UNINA9911019771503321"]
[null,null,"Autore",null,"Caers Jef"]
[null,null,"Titolo",null,"Modeling uncertainty in the earth sciences / / Jef Caers"]
[null,null,"Pubbl/distr/stampa",null,"Hoboken, N.J., : Wiley, 2011"]
[null,null,"ISBN",null,"9786613177971"]
[{"$nulls":4},"9781283177979"]
[{"$nulls":4},"1283177978"]
[{"$nulls":4},"9781119998716"]
[{"$nulls":4},"1119998719"]
[{"$nulls":4},"9781119995937"]
[{"$nulls":4},"1119995930"]
[{"$nulls":4},"9781119995920"]
[{"$nulls":4},"1119995922"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (240 p.)"]
[null,null,"Disciplina",null,"551.01/5195"]
[null,null,"Soggetti",null,"Geology - Mathematical models"]
[{"$nulls":4},"Earth sciences - Statistical methods"]
[{"$nulls":4},"Three-dimensional imaging in geology"]
[{"$nulls":4},"Uncertainty"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Intro -- Modeling Uncertainty in the Earth Sciences -- Contents -- Preface -- Acknowledgements -- 1 Introduction -- 1.1 Example Application -- 1.1.1 Description -- 1.1.2 3D Modeling -- 1.2 Modeling Uncertainty -- Further Reading -- 2 Review on Statistical Analysis and Probability Theory -- 2.1 Introduction -- 2.2 Displaying Data with Graphs -- 2.2.1 Histograms -- 2.3 Describing Data with Numbers -- 2.3.1 Measuring the Center -- 2.3.2 Measuring the Spread -- 2.3.3 Standard Deviation and Variance -- 2.3.4 Properties of the Standard Deviation -- 2.3.5 Quantiles and the QQ Plot -- 2.4 Probability -- 2.4.1 Introduction -- 2.4.2 Sample Space, Event, Outcomes -- 2.4.3 Conditional Probability -- 2.4.4 Bayes' Rule -- 2.5 Random Variables -- 2.5.1 Discrete Random Variables -- 2.5.2 Continuous Random Variables -- 2.5.2.1 Probability Density Function (pdf) -- 2.5.2.2 Cumulative Distribution Function -- 2.5.3 Expectation and Variance -- 2.5.3.1 Expectation -- 2.5.3.2 Population Variance -- 2.5.4 Examples "]
[{"$nulls":4},"of Distribution Functions -- 2.5.4.1 The Gaussian (Normal) Random Variable and Distribution -- 2.5.4.2 Bernoulli Random Variable -- 2.5.4.3 Uniform Random Variable -- 2.5.4.4 A Poisson Random Variable -- 2.5.4.5 The Lognormal Distribution -- 2.5.5 The Empirical Distribution Function versus the Distribution Model -- 2.5.6 Constructing a Distribution Function from Data -- 2.5.7 Monte Carlo Simulation -- 2.5.8 Data Transformations -- 2.6 Bivariate Data Analysis -- 2.6.1 Introduction -- 2.6.2 Graphical Methods: Scatter plots -- 2.6.3 Data Summary: Correlation (Coefficient) -- 2.6.3.1 Definition -- 2.6.3.2 Properties of r -- Further Reading -- 3 Modeling Uncertainty: Concepts and Philosophies -- 3.1 What is Uncertainty? -- 3.2 Sources of Uncertainty -- 3.3 Deterministic Modeling -- 3.4 Models of Uncertainty -- 3.5 Model and Data Relationship."]
[{"$nulls":4},"3.6 Bayesian View on Uncertainty -- 3.7 Model Verification and Falsification -- 3.8 Model Complexity -- 3.9 Talking about Uncertainty -- 3.10 Examples -- 3.10.1 Climate Modeling -- 3.10.1.1 Description -- 3.10.1.2 Creating Data Sets Using Models -- 3.10.1.3 Parameterization of Subgrid Variability -- 3.10.1.4 Model Complexity -- 3.10.2 Reservoir Modeling -- 3.10.2.1 Description -- 3.10.2.2 Creating Data Sets Using Models -- 3.10.2.3 Parameterization of Subgrid Variability -- 3.10.2.4 Model Complexity -- Further Reading -- 4 Engineering the Earth: Making Decisions Under Uncertainty -- 4.1 Introduction -- 4.2 Making Decisions -- 4.2.1 Example Problem -- 4.2.2 The Language of Decision Making -- 4.2.3 Structuring the Decision -- 4.2.4 Modeling the Decision -- 4.2.4.1 Payoffs and Value Functions -- 4.2.4.2 Weighting -- 4.2.4.3 Trade-Offs -- 4.2.4.4 Sensitivity Analysis -- 4.3 Tools for Structuring Decision Problems -- 4.3.1 Decision Trees -- 4.3.2 Building Decision Trees -- 4.3.3 Solving Decision Trees -- 4.3.4 Sensitivity Analysis -- Further Reading -- 5 Modeling Spatial Continuity -- 5.1 Introduction -- 5.2 The Variogram -- 5.2.1 Autocorrelation in 1D -- 5.2.2 Autocorrelation in 2D and 3D -- 5.2.3 The Variogram and Covariance Function -- 5.2.4 Variogram Analysis -- 5.2.4.1 Anisotropy -- 5.2.4.2 What is the Practical Meaning of a Variogram? -- 5.2.5 A Word on Variogram Modeling -- 5.3 The Boolean or Object Model -- 5.3.1 Motivation -- 5.3.2 Object Models -- 5.4 3D Training Image Models -- Further Reading -- 6 Modeling Spatial Uncertainty -- 6.1 Introduction -- 6.2 Object-Based Simulation -- 6.3 Training Image Methods -- 6.3.1 Principle of Sequential Simulation -- 6.3.2 Sequential Simulation Based on Training Images -- 6.3.3 Example of a 3D Earth Model -- 6.4 Variogram-Based Methods -- 6.4.1 Introduction -- 6.4.2 Linear Estimation."]
[{"$nulls":4},"6.4.3 Inverse Square Distance -- 6.4.4 Ordinary Kriging -- 6.4.5 The Kriging Variance -- 6.4.6 Sequential Gaussian Simulation -- 6.4.6.1 Kriging to Create a Model of Uncertainty -- 6.4.6.2 Using Kriging to Perform (Sequential) Gaussian Simulation -- Further Reading -- 7 Constraining Spatial Models of Uncertainty with Data -- 7.1 Data Integration -- 7.2 Probability-Based Approaches -- 7.2.1 Introduction -- 7.2.2 Calibration of Information Content -- 7.2.3 Integrating Information Content -- 7.2.4 Application to Modeling Spatial Uncertainty -- 7.3 Variogram-Based Approaches -- 7.4 Inverse Modeling Approaches -- 7.4.1 Introduction -- 7.4.2 The Role of Bayes' Rule in Inverse Model Solutions -- 7.4.3 Sampling Methods -- 7.4.3.1 Rejection Sampling -- 7.4.3.2 Metropolis Sampler -- 7.4.4 Optimization Methods -- Further Reading -- 8 Modeling Structural Uncertainty -- 8.1 Introduction -- 8.2 Data for Structural Modeling in the Subsurface -- 8.3 Modeling a Geological Surface -- 8.4 Constructing a Structural Model -- 8.4.1 Geological Constraints and Consistency -- 8.4.2 Building the Structural Model -- 8.5 Gridding the "]
[{"$nulls":4},"Structural Model -- 8.5.1 Stratigraphic Grids -- 8.5.2 Grid Resolution -- 8.6 Modeling Surfaces through Thicknesses -- 8.7 Modeling Structural Uncertainty -- 8.7.1 Sources of Uncertainty -- 8.7.2 Models of Structural Uncertainty -- Further Reading -- 9 Visualizing Uncertainty -- 9.1 Introduction -- 9.2 The Concept of Distance -- 9.3 Visualizing Uncertainty -- 9.3.1 Distances, Metric Space and Multidimensional Scaling -- 9.3.2 Determining the Dimension of Projection -- 9.3.3 Kernels and Feature Space -- 9.3.4 Visualizing the Data-Model Relationship -- Further Reading -- 10 Modeling Response Uncertainty -- 10.1 Introduction -- 10.2 Surrogate Models and Ranking -- 10.3 Experimental Design and Response Surface Analysis -- 10.3.1 Introduction."]
[{"$nulls":4},"10.3.2 The Design of Experiments -- 10.3.3 Response Surface Designs -- 10.3.4 Simple Illustrative Example -- 10.3.5 Limitations -- 10.4 Distance Methods for Modeling Response Uncertainty -- 10.4.1 Introduction -- 10.4.2 Earth Model Selection by Clustering -- 10.4.2.1 Introduction -- 10.4.2.2 k-Means Clustering -- 10.4.2.3 Clustering of Earth Models for Response Uncertainty Evaluation -- 10.4.3 Oil Reservoir Case Study -- 10.4.4 Sensitivity Analysis -- 10.4.5 Limitations -- Further Reading -- 11 Value of Information -- 11.1 Introduction -- 11.2 The Value of Information Problem -- 11.2.1 Introduction -- 11.2.2 Reliability versus Information Content -- 11.2.3 Summary of the VOI Methodology -- 11.2.3.1 Steps 1 and 2: VOI Decision Tree -- 11.2.3.2 Steps 3 and 4: Value of Perfect Information -- 11.2.3.3 Step 5: Value of Imperfect Information -- 11.2.4 Value of Information for Earth Modeling Problems -- 11.2.5 Earth Models -- 11.2.6 Value of Information Calculation -- 11.2.7 Example Case Study -- 11.2.7.1 Introduction -- 11.2.7.2 Earth Modeling -- 11.2.7.3 Decision Problem -- 11.2.7.4 The Possible Data Sources -- 11.2.7.5 Data Interpretation -- Further Reading -- 12 Example Case Study -- 12.1 Introduction -- 12.1.1 General Description -- 12.1.2 Contaminant Transport -- 12.1.3 Costs Involved -- 12.2 Solution -- 12.2.1 Solving the Decision Problem -- 12.2.2 Buying More Data -- 12.2.2.1 Buying Geological Information -- 12.2.2.2 Buying Geophysical Information -- 12.3 Sensitivity Analysis -- Index."]
[null,null,null,"Sommario/riassunto","'Modeling Uncertainty in the Earth Sciences' highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex earth systems and the impact that it has on practical situations."]