Optimization methods

2022/2023
Programme:
Financial mathematics, First Cycle
Year:
1 year
Semester:
second
Kind:
mandatory
ECTS:
6
Language:
slovenian
Hours per week – 2. semester:
Lectures
3
Seminar
0
Tutorial
3
Lab
0
Content (Syllabus outline)

Optimization problems, examples.
Local optimization.
Linear programming, simplex method, dual problem.
Discrete optimization problems.
Transshipment problem, matchings and coverings, network flow, minimum spanning tree. Convex problems. Karush-Kuhn-Tucker theorem.

Readings

V. Batagelj: Optimizacijske metode, Zapiski predavanj, Ljubljana.http://vlado.fmf.uni-lj.si/vlado/optim/opt1.pdfhttp://vlado.fmf.uni-lj.si/vlado/optim/lp.pdf
V. Batagelj, M. Kaufman: Naloge iz optimizacijskih metod, Ljubljana.http://vlado.fmf.uni-lj.si/vlado/optim/optnal.pdf
Jiří Matoušek, Bernd Gärtner: Understanding and Using LinearProgramming, Springer 2007
Vašek Chvátal: Linear Programming, W. H. Freeman and Co., New York, 1983
Stephen Boyd, Lieven Vandenberghe: Convex Optimization, CambridgeUniversity Press, Cambridge, 2004

Objectives and competences

To provide a basic knowledge on optimization problems, linear programming, discrete optimization and convex optimization.

Intended learning outcomes

Knowledge and understanding: The student obtains basic knowledge about linear programming, graph algorithms and convex optimization. He or she is familiar with basic optimization methods and knows how to solve them with a computer.
Application: Solving optimization problems in economics, finance and operations research.
Reflection: The importance of modelling of problems for their effective resolution.
Transferable skills: The ability to present various everyday problems in the form of mathematical optimization tasks. Ability to use computer programs to solve basic optimization problems.

Learning and teaching methods

Lectures, exercises, computer sessions, consultations

Assessment

Written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Sergio Cabello:
CABELLO, Sergio, ROTE, Günter. Obnoxious centers in graphs. SIAM journal on discrete mathematics, ISSN 0895-4801, 2010, vol. 24, no. 4, str. 1713-1730. [COBISS-SI-ID 15762265]
BUCHIN, Kevin, CABELLO, Sergio, GUDMUNDSSON, Joachim, LÖFFLER, Maarten, LUO, Jun, ROTE, Günter, SILVEIRA, Rodrigo I., SPECKMANN, Bettina, WOLLE, Thomas. Finding the most relevant fragments in networks. Journal of graph algorithms and applications, ISSN 1526-1719, 2010, vol. 14, no. 2, str. 307-336. [COBISS-SI-ID 15629401]
CABELLO, Sergio, DÍAZ-BÁÑEZ, José Miguel, LANGERMAN, Stefan, SEARA, Carlos, VENTURA, Inma. Facility location problems in the plane based on reverse nearest neighbor queries. European journal of operational research, ISSN 0377-2217. [Print ed.], 2010, vol. 202, iss. 1, str. 99-106. [COBISS-SI-ID 15160921]