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Instructors: Prof. Dr. rer. nat. Alexandra Schwartz
Event type:
Lecture & Exercise
Org-unit: Dept. 04 - Mathematics
Displayed in timetable as:
04-10-0527-vu
Subject:
Crediting for:
Hours per week:
3
Language of instruction:
German
Min. | Max. participants:
- | -
Digital Teaching:
This course takes place completely online:
- You can find all material (lecture notes, exercises, videos of the lectures, ...) in the corrresponding moodle course.
- The lecture takes place every week via Zoom.
- The exercises are discusses every second week via Zoom.
- In those weeks, where we do not discuss exercises, there are Zoom question hours, where you can ask anything regarding the lecture, exercises, ...
Course Contents:
- examples and applications
- different formulations of equilibrium constraints
- several subdifferentials (Frechet, Clarke, Mordukhovich), normal cones and optimality conditions
- solution algorithms such as penalty and regularization methods
Literature:
- Luo, Pang, Ralph: Mathematical Programs with Equilibrium Constraints, Cambridge University Press
- Outrata, Kocvara, Zowe: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints, Kluwer Academic Publishers
- Mordukhovich: Variational Analysis and Generalized Differentiation I and II, Springer
Preconditions:
It is helpful, if you have attended at least one of the following courses:
- Nonlinear Optimization
- Nonsmooth Optimization
- Nonsmooth Analysis
- Game theory
(participation without certification of prerequisites is possible)
Official Course Description:
In the lecture "Mathematical Programs with Equilibrium Constraints" we take a closer look at this class of optimization problems, called MPECs for short. Due to the special structure of the equilibrium constraints, well known optimality conditions from nonlinear optimization do not work anymore. Thus, MPECs require a specialized optimality theory, which uses methods from nonsmooth analysis, and tailored solution algorithms.
Additional Information:
The lecture is given in English in the winter term 2020/21.
Online Offerings:
moodle
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