Universität Wien FIND

Due to the COVID-19 pandemic, changes to courses and exams may be necessary at short notice (e.g. cancellation of on-site teaching and conversion to online exams). Register for courses/exams via u:space, find out about the current status on u:find and on the moodle learning platform. NOTE: Courses where at least one unit is on-site are currently marked "on-site" in u:find.

Further information about on-site teaching and access tests can be found at https://studieren.univie.ac.at/en/info.

Warning! The directory is not yet complete and will be amended until the beginning of the term.

040914 UK Applied Optimization (2020W)

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


Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first serve).


max. 30 participants
Language: German


Classes (iCal) - next class is marked with N

Tuesday 06.10. 09:45 - 11:15 Digital
Tuesday 13.10. 09:45 - 11:15 Digital
Tuesday 20.10. 09:45 - 11:15 Digital
Tuesday 27.10. 09:45 - 11:15 Digital
Tuesday 03.11. 09:45 - 11:15 Digital
Tuesday 10.11. 09:45 - 11:15 Digital
Tuesday 17.11. 09:45 - 11:15 Digital
Tuesday 24.11. 09:45 - 11:15 Digital
Tuesday 01.12. 09:45 - 11:15 Digital
Tuesday 15.12. 09:45 - 11:15 Digital
Tuesday 12.01. 09:45 - 11:15 Digital
Tuesday 19.01. 09:45 - 11:15 Digital
Tuesday 26.01. 09:45 - 11:15 Digital


Aims, contents and method of the course

Full digital synchronous mode (e-meet the professor live every week; recording is not guaranteed!)

Platform is moodle:



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) Active virtual cooperation during e-class will be awarded by up to 15 points, depending on the intensity and relevance of your communication (e.g., questions regarding administration won't be relevant for grading)

(2) virtual-oral presentation of an exercise(from the lecture notes, to be prepared in advance; format: a single .pdf with your name, max.size 5MB) which will be awarded by up to 25 points.

(3) a take-home exam on 19 January 2021 (during course hours).
Net working time will be set tight, so I suggest to prepare well (from experience, you will lack time to find the answer during exam without having thought of the topic before).
Exam will be awarded by up to 30 points.

(4) To pass the exam/course successfully, you need 31 points.


0-30: nicht genuegend/fail (5)
31-40: genuegend/pass (4)
41-50: befriedigend/satisfactory (3)
51-60: gut/good (2)
61-70: sehr gut/excellent (1)

Minimum requirements and assessment criteria

see above

Examination topics

all material presented in the course

Reading list

all material covered by lecture notes (see moodle)

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

Association in the course directory

Last modified: Tu 17.11.2020 12:27