Advances in Mathematical Modeling Optimization and Optimal Control 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.