Lehrende: Prof. Dr. Winnifried Wollner
Veranstaltungsart: Vorlesung
Anzeige im Stundenplan: M-MMOA-V
Semesterwochenstunden: 4
Unterrichtssprache: Deutsch
Min. | Max. Teilnehmerzahl: 10 | -
Kommentare/ Inhalte: Content of this lecture are analysis and numerical solution of optimization problems, where complex physical processes, usually modelled by (partial) differential equations, have to be taken into account. In contrast to classical finite dimensional optimization, these problems have an inherent infinite dimensional structure, due to the presence of differential equations. Thus, their analysis requires a mixture of functional analytic tools are techniques from optimization, and their efficient numerical solution involves the combination of algorithms and discretization methods. Aim of this lecture is to give an introduction to this lively research topic in which analysis, optimization and numerics meet.
Literatur: The lecture is not oriented at a particular book, but the following books cover wide parts of the content: Hinze, Pinnau, Ulbrich, Ulbrich: Optimization with PDE Constraints Tröltzsch: Optimal Control of Partial Differential Equations / Optimale Steuerung partieller Differentialgleichungen Ekeland/Temam: Convex Analysis and Variational Problems The following books cover analytic and numerical basics, but maybe you have a different favourite book on these topics: Rudin: Functional Analysis Rudin: Real and Complex Analysis (good introduction to integration) Conway: A Course in Functional Analysis Werner: Funktionalanalysis Werner: Einführung in die Höhere Analysis (brief account of topology, integration, functional analysis) Braess: Finite Elements / Finite Elemente Ciarlet: The Finite Element Method for Elliptic Problems (classic in finite element theory) Deuflhard: Numerical Analysis in Modern Scientific Computing I / Numerische Mathematik I (numerical basics) Nocedal/Wright: Numerical Optimization (finite dimensional optimization) Adams: Sobolev Spaces (reference book for Sobolev spaces) The following books contain further reading and may be of interest to you in the future Zeidler: Applied Functional Analysis v. 108/109 Zeidler: Nonlinear Functional Analysis and its Applications I-IV, in particular III Borwein/Zhu: Techniques of Variational Analysis Dacorogna: Direct Methods in the Calculus of Variations Struwe: Variational Methods Ito/Kunisch: Lagrange Multiplier Approach to Variational Problems and Applications
Modulkürzel: Ma-M-MMOA
Zusätzliche Hinweise zu Prüfungen: Homework: * There is a weekly homework sheet. * All exercises may be solved in teams of at most three people. Examn: * At the end of the term there is an examn, which has to be passed to get a certificate. Condition for participation is that at least 50% of the homework credit points have been reached. * Date and time of the examn are shortly after the end of the semester. The exact date is to be announced. * Certificates have a grade, according to the grade reached at the examn. Criteria for the certificate: * Active contribution in the tutorial * 50 % of the total number of homework points * Examn successfully passed
