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Deterministic and Stochastic Optimal Control and Inverse Problems [Kõva köide]

Edited by (Rochester Inst of Tech, USA), Edited by (Jagiellonian University, Poland), Edited by (Rochester Ins of Tech, USA), Edited by (The Nat Distance Education Uni, Spain)
  • Formaat: Hardback, 380 pages, kõrgus x laius: 234x156 mm, kaal: 766 g, 5 Tables, black and white; 10 Line drawings, color; 7 Line drawings, black and white; 15 Halftones, color; 4 Halftones, black and white; 25 Illustrations, color; 11 Illustrations, black and white
  • Ilmumisaeg: 15-Dec-2021
  • Kirjastus: CRC Press
  • ISBN-10: 0367506300
  • ISBN-13: 9780367506308
Teised raamatud teemal:
Deterministic and Stochastic Optimal Control and Inverse ProblemsSuurem pilt
  • Formaat: Hardback, 380 pages, kõrgus x laius: 234x156 mm, kaal: 766 g, 5 Tables, black and white; 10 Line drawings, color; 7 Line drawings, black and white; 15 Halftones, color; 4 Halftones, black and white; 25 Illustrations, color; 11 Illustrations, black and white
  • Ilmumisaeg: 15-Dec-2021
  • Kirjastus: CRC Press
  • ISBN-10: 0367506300
  • ISBN-13: 9780367506308
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367506308.html
Märksõnad:
"The inverse problem of identifying random parameters and random initial/boundary conditions in stochastic partial differential equations is a vibrant and emerging research domain that has found numerous applications. Another related problem that also ofparamount importance is the optimal control problem in stochastic PDEs. This edited volume aims to collect contributions from world-renowned researchers in the subject of stochastic control and inverse problems. We anticipate ten to fifteen contributionson stochastic optimal control and stochastic inverse problems covering various aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume will also present some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all the manuscripts will be thoroughly reviewed"--
Preface iv
Contributors xiii
1 All-At-Once Formulation Meets the Bayesian Approach: A Study of Two Prototypical Linear Inverse Problems
1(44)
Anna Schlintl
Barbara Kaltenbacher
1.1 Introduction
1(4)
1.1.1 Examples
3(2)
1.2 Function Space Setting and Computation of Adjoints
5(3)
1.2.1 Inverse Source Problem
5(1)
1.2.2 Backwards Heat Problem
6(2)
1.3 Analysis of the Eigenvalues
8(11)
1.3.1 Inverse Source Problem
10(1)
1.3.1.1 Analytic Computation of the Eigenvalues
10(1)
1.3.1.2 Numerical Computation of the Eigenvalues
11(1)
1.3.2 Backwards Heat Equation
12(2)
1.3.2.1 Analytic Computation of the Eigenvalues
14(2)
1.3.2.2 Numerical Computation of the Eigenvalues
16(3)
1.4 Convergence Analysis
19(4)
1.4.1 Fulfillment of the Link Condition for the All-At-Once-Formulation
22(1)
1.5 Choice of Joint Priors
23(6)
1.5.1 Block Diagonal Priors Satisfying Unilateral Link Estimates
23(3)
1.5.2 Heuristic Choice of C0 for the Backwards Heat Problem
26(2)
1.5.3 Priors for the Inverse Source Problem
28(1)
1.5.4 Prior for the State Variable of the Backwards Heat Problem
28(1)
1.6 Numerical Experiments
29(11)
1.6.1 Lagrangian Method for Computing the Adjoint Based Hessian and Gradient
30(3)
1.6.1.1 Inverse Source Problem
33(1)
1.6.1.2 Backwards Heat Problem
33(1)
1.6.2 Implementation
34(1)
1.6.2.1 Inverse Source Problem
35(1)
1.6.2.2 Backwards Heat Equation, Sampled Initial Condition
36(2)
1.6.2.3 Backwards Heat Equation, Chosen Initial Condition
38(1)
1.6.2.4 Backwards Heat Equation, Chosen Initial Condition, Prior Motivated by the Link Condition
39(1)
1.7 Conclusions and Remarks
40(5)
References
42(3)
2 On Iterated Tikhonov Kaczmarz Type Methods for Solving Systems of Linear Ill-posed Operator Equations
45(16)
R. Filippozzi
J.C. Rabelo
A. Leitao
2.1 Introduction
45(3)
2.2 A Range-relaxed Iterated Tikhonov Kaczmarz Method
48(6)
2.2.1 Main Assumptions
49(1)
2.2.2 Description of the Method
49(2)
2.2.3 Preliminary Results
51(3)
2.3 A Convergence Result for Exact Data
54(1)
2.4 Numerical Experiments
55(2)
2.5 Conclusions
57(4)
References
59(2)
3 On Numerical Approximation of Optimal Control for Stokes Hemivariational Inequalities
61(18)
Xiaoliang Cheng
Rongfang Gong
Weimin Han
3.1 Introduction
61(2)
3.2 Notation and Preliminaries
63(1)
3.3 Stokes Hemivariational Inequality and Optimal Control
64(3)
3.4 Numerical Approximation of the Optimal Control Problem
67(12)
References
76(3)
4 Nonlinear Tikhonov Regularization in Hilbert Scales with Oversmoothing Penalty: Inspecting Balancing Principles
79(33)
Bernd Hofmann
Christopher Hofmann
Peter Mathe
Robert Plato
4.1 Introduction
79(3)
4.1.1 Hilbert Scales with Respect to an Unbounded Operator
80(1)
4.1.2 Tikhonov Regularization with Smoothness Promoting Penalty
80(1)
4.1.3 State of the Art
81(1)
4.1.4 Goal of the Present Study
82(1)
4.2 General Error Estimate for Tikhonov Regularization in Hilbert Scales with Oversmoothing Penalty
82(3)
4.2.1 Smoothness in Terms of Source Conditions
83(1)
4.2.2 Error Decomposition
83(2)
4.3 Balancing Principles
85(12)
4.3.1 Quasi-optimality
86(1)
4.3.2 The Balancing Principles: Setup and Formulation
87(6)
4.3.3 Discussion
93(3)
4.3.4 Specific Impact on Oversmoothing Penalties
96(1)
4.4 Exponential Growth Model: Properties and Numerical Case Study
97(15)
4.4.1 Properties
97(6)
4.4.2 Numerical Case Study
103(6)
References
109(3)
5 An Optimization Approach to Parameter Identification in Variational Inequalities of Second Kind-II
112(19)
Joachim Gwinner
5.1 Introduction
112(2)
5.2 Some Variational Inequalities and an Abstract Framework for Parameter Identification
114(2)
5.3 The Regularization Procedure
116(5)
5.3.1 Smoothing the Modulus Function
116(2)
5.3.2 Regularizing the VI of Second Kind
118(3)
5.3.3 An Estimate of the Regularization Error
121(1)
5.4 The Optimization Approach
121(5)
5.5 Concluding Remarks---An Outlook
126(5)
References
128(3)
6 Generalized Variational-hemivariational Inequalities in Fuzzy Environment
131(19)
Shengda Zeng
Jinxia Cen
Stanislaw Migorski
Van Thien Nguyen
6.1 Introduction
131(2)
6.2 Mathematical Prerequisites
133(2)
6.3 Fuzzy Variational-hemivariational Inequalities
135(8)
6.4 Optimal Control Problem
143(7)
References
147(3)
7 Boundary Stabilization of the Linear MGT Equation with Feedback Neumann Control
150(20)
Marcelo Bongarti
Irena Lasiecka
7.1 Introduction
150(6)
7.1.1 The Linearized PDE Model with Space-dependent Viscoelasticity
152(1)
7.1.2 Main Results and Discussion
153(3)
7.2 Wellposedness: Proof of Theorem 7.1.2
156(14)
7.2.1 Stabilization in H: Proof of Theorem 7.1.5
159(6)
References
165(5)
8 Sweeping Process Arguments in the Analysis and Control of a Contact Problem
170(27)
Mircea Sofonea
Ti-bin Xiao
8.1 Introduction
170(2)
8.2 Notation and Preliminaries
172(3)
8.3 The Contact Model
175(4)
8.4 An Existence and Uniqueness Result
179(4)
8.5 A Continuous Dependence Result
183(5)
8.6 An Optimal Control Problem
188(4)
8.7 Conclusion
192(5)
References
194(3)
9 Anderson Acceleration for Degenerate and Nondegenerate Problems
197(20)
Sara Pollock
9.1 Introduction
197(3)
9.1.1 Mathematical Setting and Algorithm
198(1)
9.1.2 The Nondegeneracy Condition
199(1)
9.2 Nondegenerate Problems
200(5)
9.2.1 Relating Residuals to Differences Between Consecutive Iterates
202(1)
9.2.2 Full Residual Bound
203(1)
9.2.3 Numerical Examples (Nondegenerate)
204(1)
9.3 Degenerate Problems
205(8)
9.3.1 Scalar AA-Newton
206(1)
9.3.2 Methods for Higher-order Roots
207(1)
9.3.3 Analysis of the AA-Newton Rootfinding Method
208(3)
9.3.4 Numerical Examples (Degenerate)
211(1)
9.3.4.1 Example 1
212(1)
9.3.4.2 Example 2
212(1)
9.4 Conclusion
213(4)
References
214(3)
10 Approximate Coincidence Points for Single-valued Maps and Aubin Continuous Set-valued Maps
217(24)
Mohamed Ait Mansour
Mohamed Amin Bahraoui
Adham El Bekkali
10.1 Introduction
217(2)
10.2 Notation
219(3)
10.3 Coincidence and Approximate Coincidence Points of Single-valued Maps
222(6)
10.4 An Application: Parametric Abstract Systems of Equations
228(3)
10.5 Approximate Local Contraction Mapping Principle and ε-Fixed Points
231(2)
10.6 Lyusternik-Graves Theorem and e-Fixed Points for Aubin Continuous Set-valued Maps
233(8)
References
239(2)
11 Stochastic Variational Approach for Random Cournot-Nash Principle
241(29)
Annamaria Barbagallo
Massimiliano Ferrara
Paolo Mauro
11.1 Introduction
241(2)
11.2 The Random Model
243(5)
11.3 Existence Results
248(2)
11.4 The Infinite-dimensional Duality Theory
250(1)
11.5 The Lagrange Formulation of the Random Model
251(7)
11.6 The Inverse Problem
258(4)
11.7 A Numerical Example
262(4)
11.8 Concluding Remarks
266(4)
References
267(3)
12 Augmented Lagrangian Methods For Optimal Control Problems Governed by Mixed Variational-Hemivariational Inequalities Involving a Set-valued Mapping
270(33)
O. Chadli
R.N. Mohapatra
12.1 Introduction
270(2)
12.2 Problem Statement and Preliminaries
272(7)
12.3 Existence Results for Solutions
279(6)
12.4 Optimal Control
285(8)
12.5 Application to Optimal Control of a Frictional Contact Problem
293(4)
12.6 Remarks and Comments
297(6)
References
299(4)
13 Data Driven Reconstruction Using Frames and Riesz Bases
303(16)
Andrea Aspri
Leon Frischauf
Yury Korolev
Otmar Scherzer
13.1 Introduction
303(1)
13.2 Gram-Schmidt Orthonormalization
304(2)
13.2.1 Weak Convergence
306(1)
13.3 Basics on Frames and Riesz-Bases
306(2)
13.4 Data Driven Regularization by Frames and Riesz Bases
308(2)
13.4.1 Weak Convergence
309(1)
13.5 Numerical Experiments
310(5)
13.5.1 Orthonormalization Procedures
311(2)
13.5.2 Comparison Between Frames and Decomposition Algorithms
313(2)
13.6 Conclusions
315(4)
References
317(2)
14 Antenna Problem Induced Regularization and Sampling Strategies
319(35)
Willi Freeden
14.1 Uni-Variate Antenna Problem Induced Recovery Strategies
319(8)
14.2 Multi-Variate Antenna Problem Induced Recovery Strategies
327(27)
References
345(9)
15 An Equation Error Approach for Identifying a Random Parameter in a Stochastic Partial Differential Equation
354(25)
Baasansuren Jadamba
Akhtar A. Khan
Quinn T. Kolt
Miguel Sama
15.1 Introduction
354(2)
15.2 Solvability of the Direct Problem
356(4)
15.3 Numerical Techniques for Stochastic PDEs
360(2)
15.3.1 Monte Carlo Finite Element Type Methods
360(1)
15.3.2 The Stochastic Collocation Method
361(1)
15.3.3 The Stochastic Galerkin Method
361(1)
15.4 An Equation Error Approach
362(2)
15.5 Discrete Formulae
364(5)
15.6 Computational Experiments
369(3)
15.7 Concluding Remarks
372(7)
References
374(5)
Index 379
Baasansuren Jadamba is an Associate Professor at the Rochester Institute of Technology. She received her Ph.D. from Friedrich-Alexander University Erlangen-Nuremberg in 2004. Her research interests are numerical analysis of partial differential equations, finite element methods, parameter identification problems in partial differential equations, and stochastic equilibrium problems.

Akhtar A. Khan is a Professor at the Rochester Institute of Technology. His research deals with set-valued Optimization, inverse problems, and variational inequalities. He is a co-author of Set-valued Optimization, Springer (2015), and Co-editor of Nonlinear Analysis and Variational Problems, Springer (2009). He is Co-Editor in Chief of the Journal of Applied and Numerical Optimization, and Editorial Board member of Optimization, Journal of Optimization Theory and Applications, and Journal of Nonlinear and Variational Analysis.

Stanisaw Migórski received his Ph.D. and Habilitation from Jagiellonian University in Krakow (JUK). Currently, he is a Full and Chair Professor of Mathematics at the Faculty of Mathematics and Computer Science at JUK. He published research work in the field of mathematical analysis and applications (partial differential equations, variational inequalities, optimal control, and Optimization). He has edited and authored books from publishers Kluwer/Plenum, Springer and Chapman & Hall.

Miguel Sama is an associate professor at Universidad Nacional Educación a Distancia (Madrid, Spain). His research is broadly on Optimization, focusing mainly on Applied Mathematics Models. His research interests are in infinite-dimensional optimization problems. They cover a wide range of theoretical and applied topics such as Ordered Vector Spaces, Set-Valued Analysis, Vector, Set-Valued Optimization, PDE-constrained Optimization, Inverse Problems, Optimal Control Problems, and Uncertainty Quantification.