Course Syllabus for


FMAN61F, 7.5 credits

Valid from: Autumn 2021
Decided by: Professor Thomas Johansson
Date of establishment: 2021-09-07

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course codes: FMAN61, MATC61
Teaching language: English


In many applications of mathematics, e.g. image analysis, control theory and time series analysis, an essential step is to choose the parameters in a model so that it fits given data as well as possible. One wants to minimize the error, measured in some way, which may be considered as a function of several variables – the parameters – that may have to satisfy further conditions – constraints. The aim of the course is to make the doctoral student familiar with the most common methods for solving optimization problems in which the parameters may vary continuously.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

Quadratic forms and matrix factorisation. Convexity. Separatting planes and Farkas' lemma. The theory of optimization with and without constraints: Lagrange functions, Kuhn-Tucker theory. Duality. Methods for optimization without constraints: line search, steepest descent, Newton methods, conjugate directions, non-linear least squares optimization. The Nelder-Mead search method without derivatives. Methods for optimization with constraints: linear optimization, the simplex method, quadratic programming, penalty and barrier methods.

Course Literature

Böiers, L.: Mathematical Methods of Optimization. 2010. ISBN 9789144070759.

Instruction Details

Types of instruction: Lectures, seminars, laboratory exercises, exercises

Examination Details

Examination formats: Written exam, written report. Programming exercise with written report.
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: Calculus and linear algebra. Sufficient background is provided, e.g., by the courses FMAA05, FMA430, and FMAF05 or FMAF10.

Further Information

Replaces FMAN60F.

Course Occasion Information

Contact and Other Information

Course coordinators:
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