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040914 UK Applied Optimization (2019W)

4.00 ECTS (2.00 SWS), SPL 4 - Wirtschaftswissenschaften
Continuous assessment of course work

Registration/Deregistration

Details

max. 30 participants
Language: German

Lecturers

Classes (iCal) - next class is marked with N

Course starts 8 October 2019

Tuesday 08.10. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 15.10. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 22.10. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 29.10. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 05.11. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 12.11. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 19.11. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 26.11. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 03.12. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 10.12. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 17.12. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 07.01. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 14.01. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 21.01. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Tuesday 28.01. 09:45 - 11:15 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock

Information

Aims, contents and method of the course

Contents:

1. Geometric foundations of duality

1.1 Convexity and minimal distance projection
1.2 Properties of the minimal distance projection
1.3 Separation of convex sets
1.4 Supporting hyperplane and Farkas' Lemma

2. The concept of duality in optimization

2.1 Lagrange duality for constrained optimization problems
2.2 Duality gap, quality guarantee, and complementary slack
2.3 Minimax, saddle points, and optimality conditions
2.4 Convex problems: Slater condition, Wolfe dual

3. Practical aspects of duality in optimization

3.1 Linear and quadratic optimization
3.2 Ascent directions for the dual function
3.3 Dual (steepest) ascent method
3.4 (Dual) cutting planes
3.5 Duality for discrete problems; branch-and-bound

Assessment and permitted materials

(1) presence during the course is compulsory and will be awarded by up to 5 points;

(2) presentation of an exercise (from the lecture notes, to be prepared in advance) is optional/voluntary and will be awarded by up to 15 points;

(3) there are two compulsory written tests:

mid-term, on Tuesday 3 December 2019, and

end term, on Tuesday 14 January 2020

Each test can be awarded by up to 50 points.

Mode: open-book test. Electronic calculators admitted, no cell phones (flight or offline mode). Net working time: 80 minutes, which will be tight, so I suggest to prepare well (from experience, you will lack time to look up too many things in books during exam).

(4) To pass the exam/course successfully, you need 53 points.

Minimum requirements and assessment criteria

see above

Examination topics

all material presented in the course

Reading list

lecture notes for the course

Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms, Wiley

Association in the course directory

Last modified: Mo 07.09.2020 15:20