# NSCPHD1118 Advanced mathematical programming: hierarchical optimization and equilibrium

Volume 2015/2016
Content

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Most optmization problems aim at maximizing/minimizing the objective function of a single player. For example, we formulate problems to determine optimal investment or portfolios strategies to maximize our profit. However, these models assume that the decisions of the rest of the players are not affected by our own decisions and obviously, this is not always the case.

The main objective of this course is to present the main mathematical tools to formulate optimization problems in which two or more decision makers with different objective function are involved. The main contents of this course are:

A. Game Theory and Equilibrium

B. Complementarity Modelling

C. Hierarchical Optimization

D. Mathematical Programming with Equilibrium Constraints

Learning Outcome

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Knowledge:
- Game theory in a mathematical programming context
- Equilibirum programming problems
- Complementarity problems
- Bilevel and multi-level problems
- Mathematical problems with equilibrium constraints

Skills:
- To formulate and solve equilibrium problems using designed solution algorithms and standard software
- To formulate and solve complementarity problems using designed solution algorithms and standard software
- To formulate and solve bi-level and multi-level optimization problems using designed solution algorithms and standard software
- To formulate and solve mathematical programming problems with equilibrium constraints using designed solution algorithms and standard software

Competences:
- To identify real-life problem in which hieralchical optimization and equilibrium theory could be applied.
- To evaluate the most suitable method to solve a given optimization problem that includes more than one decision maker.
- To critically analyze the results of hieralchical and equilibrium problems.

At least one of the following courses: Operations Research 1 (OR1), Operations Research 2 (OR2), Modelling and GAMS, Optimization and Convexity (OK)
2 x 2 hours of lectures and 1 x 2 hours of exercises/project per week for 7 weeks.
• Category
• Hours
• Exam
• 50
• Lectures
• 28
• Preparation
• 70
• Project work
• 58
• Total
• 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral examination with 30 minutes preparation time.
Exam registration requirements

The student must hand in two projects

Aid
Only certain aids allowed

During the preparation time, all written aids allowed.

In the examination, some written aids allowed (keywords, main results of projects, etc.)

Marking scale