Valid from: Autumn 2021
Decided by: Professor Thomas Johansson
Date of establishment: 2021-09-07
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
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.
Böiers, L.: Mathematical Methods of Optimization. 2010. ISBN 9789144070759.
Types of instruction: Lectures, seminars, laboratory exercises, exercises
Examination formats: Written exam, written report.
Programming exercise with written report.
Grading scale: Failed, pass
Examiner:
Assumed prior knowledge: Calculus and linear algebra. Sufficient background is provided, e.g., by the courses FMAA05, FMA430, and FMAF05 or FMAF10.
Replaces FMAN60F.
Course coordinators:
Web page: http://www.maths.lth.se/course/bigopt/