Gäller från och med: Autumn 2021
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2021-09-07
Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskoder: FMAN61, MATC61
Undervisningsspråk: 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.
Kunskap och förståelse
För godkänd kurs skall doktoranden
Färdighet och förmåga
För godkänd kurs skall doktoranden
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.
Undervisningsformer: Föreläsningar, seminarier, laborationer, övningar
Examinationsformer: Skriftlig tentamen, skriftlig rapport.
Programming exercise with written report.
Betygsskala: Underkänd, godkänd
Examinator:
Förutsatta förkunskaper: Calculus and linear algebra. Sufficient background is provided, e.g., by the courses FMAA05, FMA430, and FMAF05 or FMAF10.
Replaces FMAN60F.
Kursansvariga:
Hemsida: http://www.maths.lth.se/course/bigopt/