Linjär och kombinatorisk optimering

**Valid from:** Spring 2021**Decided by:** Professor Thomas Johansson**Date of establishment:** 2021-03-01

**Division:** Mathematics**Course type:** Course given jointly for second and third cycle**The course is also given at second-cycle level with course codes:** FMAF35, FMA240**Teaching language:** English

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 students aware of problems in linear and combinatorial optimization which are important in the applications, and to give them knowledge about mathematical methods for their solution. The aim is also to make the students develop their ability to solve problems, with and without the use of a computer.

*Knowledge and Understanding*

For a passing grade the doctoral student must

- understand and be able to clearly explain the theory behind the simplex method.
- be able to describe and informally explain the mathematical theory behind central algorithms in combinatorial optimization (including local search, branch and bound methods, simulated annealing, genetic optimization, neural networks).

*Competences and Skills*

For a passing grade the doctoral student must

- 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.

Linear programming. Integer programming. Transport problems. Assignment problems. Maximal flow. Local search. Simulated annealing. Genetic optimization. Neural networks. Dynamic programming. Algorithm complexity.

- Holmberg, K.: Optimering: metoder, modeller och teori för linjära, olinjära och kombinatoriska problem. 2010. ISBN 9789147099351.
- Kolman & Beck: Elementary Linear Programming with Applications.. Academic Press, 1995.

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

**Examination formats:** Written exam, oral exam, miscellaneous.
Computer sessions. Written and/or oral test, to be decided by the examiner. Some minor projects should be completed before the exam.**Grading scale:** Failed, pass**Examiner:**

**Assumed prior knowledge:** FMAB20 Linear Algebra.

**Course coordinators:** **Web page:** http://www.ctr.maths.lu.se/course/linkomboptnykod/