Advances in Mathematical Modeling, Optimization and Optimal Control

Description

This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development. Front Matter....Pages i-v Introduction....Pages 1-2 Bregman Distances in Inverse Problems and Partial Differential Equations....Pages 3-33 On Global Attractor for Parabolic Partial Differential Inclusion and Its Time Semidiscretization....Pages 35-64 Passive Control of Singularities by Topological Optimization: The Second-Order Mixed Shape Derivatives of Energy Functionals for Variational Inequalities....Pages 65-102 Optimal Control for Applications in Medical and Rehabilitation Technology: Challenges and Solutions....Pages 103-145 Second-Order Optimality Conditions for Broken Extremals and Bang-Bang Controls: Theory and Applications....Pages 147-201