11144nam 2200529 450 99646641980331620231110223400.03-030-79393-1(MiAaPQ)EBC6892159(Au-PeEL)EBL6892159(CKB)21271982500041(PPN)260825689(EXLCZ)992127198250004120221003d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNon-smooth and complementarity-based distributed parameter systems simulation and hierarchical optimization /edited by Michael Hintermüller, [and three others]Cham, Switzerland :Springer,[2022]©20221 online resource (518 pages)International Series of Numerical Mathematics ;v.172Print version: Hintermüller, Michael Non-Smooth and Complementarity-Based Distributed Parameter Systems Cham : Springer International Publishing AG,c2022 9783030793920 Includes bibliographical references.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 -- 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.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.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 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.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.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 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.1 Motivation and Introduction.International Series of Numerical Mathematics Distributed parameter systemsTeoria de controlthubLlibres electrònicsthubDistributed parameter systems.Teoria de control003.78Hintermüller MichaelMiAaPQMiAaPQMiAaPQBOOK996466419803316Non-smooth and complementarity-based distributed parameter systems2920122UNISA