Deterministic and Stochastic Optimal Control and Inverse Problems  book cover
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Deterministic and Stochastic Optimal Control and Inverse Problems




ISBN 9780367506308
Published December 15, 2021 by CRC Press
394 Pages 25 Color & 11 B/W Illustrations

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Book Description

Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations.

This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.

Table of Contents

1. All-At-Once Formulation Meets the Bayesian Approach: A Study of Two Prototypical Linear Inverse Problems

Anna Schlintl and Barbara Kaltenbacher

2. On Iterated Tikhonov Kaczmarz Type Methods for Solving Systems of Linear Ill-posed Operator Equations

R Filippozzi, JC Rabelo and A Leitão

3. On Numerical Approximation of Optimal Control for Stokes Hemivariational Inequalities

Xiaoliang Cheng, Rongfang Gong and Weimin Han

4. Nonlinear Tikhonov Regularization in Hilbert Scales with Oversmoothing Penalty: Inspecting Balancing Principles

Bernd Hofmann, Christopher Hofmann, Peter Mathé and Robert Plato

5. An Optimization Approach to Parameter Identification in Variational Inequalities of Second Kind-II

Joachim Gwinner

6. Generalized Variational-hemivariational Inequalities in Fuzzy Environment

Shengda Zeng , Jinxia Cen, Stanisław Migórski and Van Thien Nguyen

7. Boundary Stabilization of the Linear MGT Equation with Feedback Neumann Control

Marcelo Bongarti and Irena Lasiecka

8. Sweeping Process Arguments in the Analysis and Control of a Contact Problem

Mircea Sofonea and Yi-bin Xiao

9. Anderson Acceleration for Degenerate and Nondegenerate Problems

Sara Pollock

10. Approximate Coincidence Points for Single-valued Maps and Aubin Continuous Set-valued Maps

Mohamed Ait Mansour, Mohamed Amin Bahraoui and Adham El Bekkali

11. Stochastic Variational Approach for Random Cournot-Nash Principle

Annamaria Barbagallo, Massimiliano Ferrara and Paolo Mauro

12. Augmented Lagrangian Methods For Optimal Control Problems Governed by Mixed Variational-Hemivariational Inequalities Involving a Set-valued Mapping

O Chadli and RN Mohapatra

13. Data Driven Reconstruction Using Frames and Riesz Bases

Andrea Aspri, Leon Frischauf, Yury Korolev and Otmar Scherzer

14. Antenna Problem Induced Regularization and Sampling Strategies

Willi Freeden

15. An Equation Error Approach for Identifying a Random Parameter in a Stochastic Partial Differential Equation

Baasansuren Jadamba, Akhtar A Khan, Quinn T Kolt and Miguel Sama

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Editor(s)

Biography

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.

Stanisław 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.