Lecture course in summer term 2015:

V4E2 – Numerical Simulation

Prof. Dr. André Uschmajew

Assistent: Bastian Bohn

Requirements: Wissenschaftliches Rechnen I (V3E1/F4E1)

Description

We will introduce tools from nonlinear functional analysis to deal with optimization problems in Banach spaces. Variational methods can be considered to find extremal functions here. Optimal control problems with partial differential equations are of special interest in numerics and will serve as an example.

Date & time

Lectures:	Tue,	10:15–11:45 am,	Wegelerstr. 6, SemR We 6.020
	Thu,	8:30–10:00 am,	Wegelerstr. 6, SemR We 6.020
First lecture:	Tue,	7.4.2015
Tutorial:	Wed,	4:15–5:45 pm,	Wegelerstr. 6, SemR We 6.020
First tutorial:	Wed,	15.4.2015

Final Exam

Appointments for the final exam (oral) will be made individually by Prof. Dr. Uschmajew.

Exercise sheets

Excercise sheets will be provided on a weekly basis. Some weeks there will be programming exercises.

• Exercise Sheet 1 (corrected: 15.04. [Exercise 1: f should map into the real numbers.])
• Exercise Sheet 2
• Exercise Sheet 3 (corrected: 29.04. [Exercise 3: A square was missing in the definition of A.])
• Exercise Sheet 4
• Exercise Sheet 5
• Exercise Sheet 6 (corrected: 20.05. [Exercise 2: Added m <= n.])
• Exercise Sheet 7
• Exercise Sheet 8
• Exercise Sheet 9 (Note: The closing date for the programming exercise is 30.06.)
• Exercise Sheet 10
• Exercise Sheet 11
  

Requirements for the exam

Students need to achieve 50% of the points of the theoretical exercises for admittance to the final exam. Furthermore, the solutions will have to be presented in the tutorial at least twice during the semester from each student. A successful presentation of the results for the programming exercises is also required.

Literature

[1]	A.D. Ioffe and V.M. Tichomirov, Theorie der Extremalaufgaben, Deutscher Verlag der Wissenschaften, Berlin, Germany, 1979
[2]	A.D. Ioffe and V.M. Tihomirov, Theory of Extremal Points, North-Holland, New York, USA, 1978.
[3]	F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen: Theorie, Verfahren und Anwendungen, Vieweg+Teubner, Wiesbaden, Germany, 2009.
[4]	F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications, vol. 112 of Graduate Studies in Mathematics, American Mathematical Society, Providence, USA, 2010.
[5]	E. Zeidler, Nonlinear Functional Analysis and its Applications III - Variational Methods and Optimization, Springer, New York, USA, 1985

You can borrow books from the Library of Mathematics or the MNL Branch Library for example.