Syllabus

Title
5309 Optimization
Instructors
Niklas Hey, DPhil
Contact details
Type
PI
Weekly hours
2
Language of instruction
Englisch
Registration
02/02/26 to 02/15/26
Registration via LPIS
Notes to the course
Dates
Day Date Time Room
Tuesday 03/03/26 02:00 PM - 05:30 PM D4.0.127
Tuesday 03/10/26 02:00 PM - 05:30 PM D4.0.127
Tuesday 03/17/26 02:00 PM - 05:30 PM D4.0.127
Tuesday 03/24/26 02:00 PM - 05:30 PM D4.0.127
Tuesday 04/07/26 02:00 PM - 05:30 PM D4.0.127
Tuesday 04/14/26 02:00 PM - 05:30 PM D4.0.127
Tuesday 04/21/26 02:00 PM - 04:00 PM TC.3.05
Contents

Mathematical optimization (or mathematical programming) is a central tool for all kinds of decision-making, ranging from engineering to economics. In this course, we will focus on continuous
(non-linear) optimization and learn the basics of theory and algorithms for unconstrained and constrained optimization. We will cover topics such as


• necessary and sufficient conditions for unconstrained optimization,
• numerical methods for functions of one variable,
• gradient methods and Newton’s method for functions of multiple variables,
• Lagrange function and Lagrange multipliers of constrained optimization problem,
• Lagrange method for equality-constrained optimization,
• Karush-Kuhn-Tucker conditions for inequality-constrained optimization,
• duality.

Learning outcomes

After completing this course the student will have the ability to:

  • understand and interpret classic models in financial economics that build on an optimization argument;
  • construct economic models that imply an optimizing decision maker and perform analytical and /or numerical analysis.
  • communicate and discuss possible approaches to a certain problem in class;
  • work in groups and contribute to the implementation of economic optimization models. Defend the chosen approach in class.
  • apply methods of static and dynamic optimization to questions arising in financial economics;
Attendance requirements

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.

Teaching/learning method(s)

This course will be taught as a combination of lectures in optimization theory and the solution of homework assignments, possibly in groups.

Assessment

Grading will be determined according to the following grading scheme, each component is
described bellow:


Worksheets: 30%

Minitest during class: 10%

written final exam: 60%

 

Grades: 1: at least 90%, 2: at least 75%, 3: at least 60%, 4: at least 50%, 5: less than 50%

Prerequisites for participation and waiting lists

Mathematics and Computing courses

You should be familiar with the following from linear algebra and calculus:
• matrix operations (addition, multiplication, transposition),
• eigenvalues of a matrix,
• quadratic forms and their definiteness,
• gradient and Hessian of a function,
• (Euclidean) inner product and norm.

Readings

Please log in with your WU account to use all functionalities of read!t. For off-campus access to our licensed electronic resources, remember to activate your VPN connection connection. In case you encounter any technical problems or have questions regarding read!t, please feel free to contact the library at readinglists@wu.ac.at.

Other

R. Frey: Lecture notes Optimization, available on Canvas, 2016 (updated version 2021
by B. Rudloff).
• Bertsekas, D.: Nonlinear Programming, Athena Scientific Publishing, 1999.
• Griva, Nash, Sofer: Linear and Nonlinear Optimization, SIAM Publishing, 2009.
• Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004. (Available on author’s website https://web.stanford.edu/~boyd/cvxbook/)

Last edited: 2026-02-17



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