Linear and Combinatorial Optimization
Linjär och kombinatorisk optimering

FMAP05F, 7.5 högskolepoäng

Gäller från och med: Autumn 2022
Beslutad av: Maria Sandsten
Datum för fastställande: 2022-11-23

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMAP05
Undervisningsspråk: English

Syfte

In science, technology and economics, linear and combinatorial optimization problems appear more and more often. The most well known example is linear programming, where the so called simplex method has been of utmost importance in industry since it was invented in the middle of the 20th century. Other important problems, e.g. for effective data processing, contain discrete variables, for example integers. In connection with these, the importance of combinatorial methods has grown. The aim of the course is to make the PhD students aware of some problems in linear and combinatorial optimization which are important in applications, and to give them knowledge about modern mathematical methods for their solution. The aim is also to make the PhD student develop their ability to solve problems, with and without the use of a computer, and their ability to read mathematical texts.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• understand and be able to clearly explain the theory behind the simplex method.
• be able to describe and explain the mathematical theory behind some central algorithms in combinatorial optimization.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• be able to show a good capability to (i) identify problems in the area, (ii) formulate these in mathematical terms, (iii) choose an appropriate method to solve them, and finally (iv) carry out the solution, possibly with the help of a computer.
• be able to write computer programs to solve linear and combinatorial optimization problems.
• with proper terminology, in a well structured way and with clear logic be able to explain the solution to a problem within linear and combinatorial optimization.

Kursinnehåll

Linear programming. Integer programming. Transport problems. Assignment problems. Maximal flow. Some modern methods in combinatorial optimization. Algorithm complexity.

Kurslitteratur

Kolman, B. & Beck, R.E.: Elementary Linear Programming with Applications. Academic Press, 1995, ISBN: 0-12-417910. Available as E-book from the Maths Library. Supplementary material. B.Korte & J. Vygen: Combinatorial Optimization, Theory and Algorithms. Springer, 2019, ISBN: 9783662585665. Sixth edition. An earlier edition is available as e-book from the Mathematics Library.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, seminarier

Kursens examination

Examinationsform: Inlämningsuppgifter. Assignments.
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: FMAB20 Linear Algebra. Programming with Python or Matlab. Some course in mathematics beyond calculus in several variables (for mathematical maturity).

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://www.maths.lth.se/course/lincombopt75/