Syllabus
Registration via LPIS
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.
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;
Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.
Worksheets: Worksheets will be distributed during the lectures and you will be asked to work on them either during the lecture time or as homework. You can complete the worksheets in groups of two. The best 80% of the worksheets will count towards your grade.
Group project: You will be asked to implement numerical optimization methods studied in the course. You should work in groups of two students.
Take-home exam: You will be distributed a final exam at the end of the course and you will be asked to complete it within a week of the course ending. You are allowed to use all materials distributed during the course and your own notes while working on your exam. I ask you to maintain academic integrity and not obtain outside help either from your classmates or using the internet, i.e. AI tools.
Grading will be determined according to the following grading scheme, each component is
described bellow:
Worksheets: 30%
Group project: 30%
Take-home exam: 40%
Grades: 1: at least 90%, 2: at least 80%, 3: at least 70%, 4: at least 60%, 5: less than 60%
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.
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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/)
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