Baasansuren Jadamba (editor) - Deterministic and Stochastic Optimal Control and Inverse Problems

Editors

Baasansuren Jadamba

Rochester Institute of Technology Rochester, New York, USA

Akhtar A. Khan

Rochester Institute of Technology Rochester, New York, USA

Stanisaw Migrski

Faculty of Mathematics and Computer Science Jagiellonian University, Krakow, Poland

Miguel Sama

National Distance Education University (UNED) Madrid, Spain

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ISBN: 978-0-367-50630-8 (hbk) ISBN: 978-0-367-50631-5 (pbk) ISBN: 978-1-003-05057-5 (ebk)

DOI: 10.1201/9781003050575

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Dedicated to Zuhair Nashed on his 85th birthday

It is our immense pleasure and privilege to dedicate this volume to Professor Zuhair Nashed on the occasion of his 85th birthday. During the last almost six decades, Prof. Zuhair Nashed made fundamental contributions to strengthening various aspects of operator theory, functional analysis, numerical analysis, inverse and ill-posed problems, iterative methods, differentiability concepts, generalized inverses, variational inequalities, regularization techniques, integral equations, signal analysis, sampling theory, among others. Prof. Zuhair Nashed is the founding editor of the journal Numerical Functional Analysis and Optimization and the founding co-editor of the Journal of Integral Equations and Applications. He has published more than 150 papers in reputed journals. His original and widely cited research work remains a source of inspiration for several generations of aspirants and accomplished researchers alike. His unique scientific contributions and dynamic personality have well-deservedly made him a recipient of many accolades. The fascinating tribute by K. Atkinson and C. Groetsch Zuhair Nashed. A biographical tribute. J. Integer Eq. Appl., 20: 153160, 2008 provides details on his personal and professional accomplishments. Another beautiful tribute that offers insight into the life of Prof. Nashed is by J. Ding: A conversation with Zuhair Nashed (in Chinese). Math. Cult., 9: 4157, 2018. To gauge Prof. Nasheds impact on international research, we wish to mention the tribute by Y. Wang and Y. Wei: Special Issue Research on Generalized Inverses in China, Numerical Functional Analysis and Optimization, 41: 16691671, 2020.

Inverse problems constitute a vital area of research that possesses a toolbox of powerful theoretical tools, efficient and reliable computational techniques, and applications to a wide array of real-world problems. During the last decades, inverse problems witnessed explosive growth, and many directions of research emerged. The primary object of this volume is to present, in a unified framework, some of the recent developments in deterministic and stochastic inverse problems. This subject enjoyed Prof. Zuhair Nasheds concentrated attention and benefited from his creativity. We anticipate this volume will give a glimpse of some of the commonly pursued research directions in inverse problems and related domains.

This volume is comprised of fifteen chapters. It begins with a contribution by A. Schlintl and B. Kaltenbacher, who study the Bayesian approach to inverse problems in an all-at-once framework. R. Filippozzi, J.C. Rabelo and A. Leito propose a nonstationary iterated Tikhonov Kaczmarz method for obtaining stable approximate solutions to systems of ill-posed equations. X. Cheng, R. Gong and W. Han consider the numerical approximation of optimal control problems governed by a stationary Stokes hemivariational inequality. B. Hofmann, C. Hofmann, P. Math and R. Plato focus on some aspects of analytical developments of Tikhonov regularization for nonlinear ill-posed equations with smoothness promoting penalties. J. Gwinner develops a general framework for the inverse problem of parameter identification in variational inequalities of the second kind that treat the parameter linked to a bilinear form and a nonlinear non-smooth function. S. Zeng, J. Cen, S. Migorski and V.T. Nguyen investigate a generalized fuzzy variational-hemivariational inequality in an infinite-dimensional Banach space. M. Bongarti and I. Lasiecka study a boundary stabilization of a linearized version of the so-called JordanMooreGibsonThompson (JMGT) equation. M. Sofonea and Y. Xiao study a new mathematical model (and associated control problem) that describes the quasistatic contact of a viscoelastic body with a deformable obstacle covered by a layer of viscous fluid. S. Pollock reviews some recent developments on the acceleration properties of the extrapolation technique know as Anderson acceleration. M.A. Mansour, M.A. Bahraoui and A.E. Bekkali consider approximate coincidence points for single-valued maps and approximate fixed points for Aubin continuous set-valued maps. A. Barbagallo, M. Ferrara and P. Mauro investigate a stochastic variational inequality that models the Cournot-Nash equilibrium principle with uncertainty. O. Chadli and R.N. Mohapatra develop an augmented Lagrangian framework for optimal control problems governed by mixed variational-hemi-variational inequalities. A. Aspri, L. Frischauf, Y. Korolev and O. Scherzer study a purely data-driven regularization method for inverse problems and devise a projection algorithm with respect to frames as a data-driven reconstruction procedure in inverse problems. The work of W. Freeden deals with the Antenna problem induced regularization and sampling strategies. B. Jadamba, A.A. Khan, Q.T. Kolt and M. Sama propose a new equation error approach for identifying a random parameter in the stochastic diffusion equation.

We firmly believe that the breadth and diversity of areas covered in this volume will make it of great interest to researchers in inverse problems, optimal control, variational inequalities, optimization problems, and areas that are enriched by their applications.

A final word of gratitude is due to the researchers who contributed to this volume with their excellent contributions. We are grateful to the referees of the chapters included and Vijay Primlani for his professionalism and patience.