Kursussøgning, efter- og videreuddannelse – Københavns Universitet

Videresend til en ven Resize Print Bookmark and Share

Kursussøgning, efter- og videreuddannelse

Cancelled: Operations Research 3: Hierarchical optimization and equilibrium

Practical information
Study year 2016/2017
Block 4
Programme level Full Degree Master
Course responsible
  • Salvador Pineda Morente
  • Department of Mathematical Sciences
Course number: NMAK15001U

Course content

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

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

- 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

- 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.

Recommended prerequisites

At least one of the following courses: Operations Research 1 (OR1), Operations Research 2 (OR2), Modelling and GAMS, Optimization and Convexity (OK)

Sign up

As an exchange, guest and credit student - click here!

Continuing Education - click   here!


MSc Programme in Mathematics-Economy


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


---- SKEMA LINK ----

Teaching and learning methods

2 x 2 hours of lectures and 1 x 2 hours of exercises/project per week for 7 weeks.


no limit




Category Hours
Lectures 28
Project work 58
Exam 1
Preparation 105
Class Instruction 14
English 206


Type of assessment

Oral examination, 30 minutes
30 minutes oral examination with 30 minutes preparation time.


Only certain aids allowed

During the preparation time, all written aids allowed.

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

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the main learning objectives of the course as well as the realized projects.

Censorship form

No external censorship
Several internal examiners


As the ordinary exam. If the project was not approved before the ordinary exam it must be resubmitted at the latest two weeks before the beginning of the re-exam week. The project must be approved before the re-exam

Mere information om kurset
Er du BA- eller KA-studerende?
Er du bachelor- eller kandidat-studerende, så find dette kursus i kursusbasen for studerende:

Kursusinformation for indskrevne studerende