Jean Baptiste Hiriart Urruty Livres

L’étude mathématique des problèmes d’optimisation, ou de ceux dits variationnels de manière générale (c’est-à-dire, « toute situation où il y a quelque chose à minimiser sous des contraintes »), requiert en préalable qu’on en maîtrise les bases, les outils fondamentaux et quelques principes. Le présent ouvrage est un cours répondant en partie à cette demande, il est principalement destiné à des étudiants de Master en formation, et restreint à l’essentiel. Sont abordés successivement : La semicontinuité inférieure, les topologies faibles, les résultats fondamentaux d’existence en optimisation ; Les conditions d’optimalité approchée ; Des développements sur la projection sur un convexe fermé, notamment sur un cône convexe fermé ; L’analyse convexe dans son rôle opératoire ; Quelques schémas de dualisation dans des problèmes d’optimisation non convexe structurés ; Une introduction aux sous-différentiels généralisés de fonctions non différentiables.

This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published - by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. Now [18] hasa dual but clearly defined nature: - an introduction to the basic concepts in convex analysis, - a study of convex minimization problems (with an emphasis on numerical al- rithms), and insists on their mutual interpenetration. It is our feeling that the above basic introduction is much needed in the scientific community. This is the motivation for the present edition, our intention being to create a tool useful to teach convex anal ysis. We have thus extracted from [18] its „backbone“ devoted to convex analysis, namely ChapsIII-VI and X. Apart from some local improvements, the present text is mostly a copy of thecorresponding chapters. The main difference is that we have deleted material deemed too advanced for an introduction, or too closely attached to numerical algorithms. Further, we have included exercises, whose degree of difficulty is suggested by 0, I or 2 stars *. Finally, the index has been considerably enriched. Just as in [18], each chapter is presented as a „lesson“, in the sense of our old masters, treating of a given subject in its entirety.

This book presents 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 offers a comprehensive examination of new theoretical and application-oriented results in mathematical modeling, optimization, and optimal control. It is particularly valuable for students and researchers engaged in image processing, partial differential inclusions, shape optimization, and optimal control theory as applied to medical and rehabilitation technology. The first chapter by Martin Burger discusses recent advancements in Bregman distances, crucial for inverse problems and image processing. Piotr Kalita's chapter explores the operator version of a first-order in time partial differential inclusion and its time discretization. The chapter by Günter Leugering, Jan Sokołowski, and Antoni Żochowski addresses nonsmooth shape optimization problems related to variational inequalities. Katja Mombaur's chapter focuses on optimal control and inverse optimal control applications in medical and rehabilitation technology, particularly in human movement analysis and therapy through medical devices. The final chapter by Nikolai Osmolovskii and Helmut Maurer surveys no-gap second-order optimality conditions in the calculus of variations and optimal control, discussing their further development.