This book contains anin-depth presentation of the plenary talks given from the 16th French-German-Polish Conference onOptimization, held in Kraków, Poland in 2013. Each chapter in this book exhibitsa comprehensive look at new theoretical results and applications inmathematical modeling, optimization, and optimal control. Students andresearchers involved in image processing, partial differential inclusions,shape optimization, optimal control theory and its applications to medical andrehabilitation technology, will find this book valuable.The first chapter by Martin Burger provides an overview ofrecent developments related to Bregman distances, which are vital tool ininverse problems and image processing. The chapter by Piotr Kalita studies theoperator version of a first order in time partial differential inclusion andits time discretization. In the chapter by Günter Leugering, Jan Sokolowski andAntoni _ochowski, nonsmooth shape optimization problems for variational i
nequalitiesare considered. The next chapter, by Katja Mombaur is devoted to applicationsof optimal control and inverse optimal control in the field of medical andrehabilitation technology, in particular in human movement analysis, therapyand improvement by means of medical devices. The final chapter, by NikolaiOsmolovskii and Helmut Maurer provides a survey on no-gap second orderoptimality conditions in the calculus of variations and optimal control, and adiscussion of their further development.
Introduction. - Bregman Distances in Inverse Problems and Partial DifferentialEquations (Martin Burger).- On global attractor for parabolic partialdifferential inclusion and its time semi-discretization (Piotr Kalita). -Passive control of singularitiesby topological optimization (GünterLeugering, Jan Sokolowski and Antoni _ochowski). - Optimal Control for Applications in Medical and RehabilitationTechnology (Katja Mombaur). - Second-Order OptimalityConditions for Broken Extremals and Bang-Bang Controls ( Nikolai P. Osmolovskii and Helmut Maurer).
