Topics in optimization

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
R1
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

The lecturer selects some important topics in optimization, such as:
Mathematical foundations of interior-point methods.
Advanced problems of combinatorial optimization.
Integer programming.
Iterative methods in optimization.
Heuristics, evolutionary and genetic programming.
Applications of optimization methods in finance, economy, logistics, telecommunications, etc.
Stochastic programming, etc.

Readings

S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge University Press, Cambridge, 2004.
J. Renegar: A Mathematical View of Interior-Point Methods in Convex Optimization, Society for Industrial and Applied Mathematics, Philadelphia, 2001.
B. H. Korte, J. Vygen: Combinatorial Optimization: Theory and Algorithms, 3. izdaja, Springer, Berlin, 2006.
L. A Wolsey: Integer Programming, Wiley, New York, 1998.
C. T. Kelley: Iterative Method for Optimization, Society for Industrial and Applied Mathematics, Philadelphia, 1999.
Z. Michalewicz, D. B. Fogel: How to Solve It: Modern Heuristics, 2. izdaja, Springer, Berlin, 2004.

Objectives and competences

Students become acquainted with one or several of the more important areas of optimization.

Intended learning outcomes

Knowledge and understanding: Students gain deeper knowledge of selected optimization areas. They become familiar with both the theoretical foundations and the techniques for solving optimization problems in these areas.Application: Solving optimization problems which arise in practice.Reflection: The importance of adequate modelling of optimization problems which facilitates their efficient solving.Transferable skills: Capabilities to model practical problems as mathematically formulated optimization problems, to distinguish between computationally feasible and infeasible problems, to construct models and to analyze them by means of appropriate software tools.

Learning and teaching methods

Lectures, seminar, exercises, homework, consultations, and independent work by the students

Assessment

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Sergio Cabello:
CABELLO, Sergio, DÍAZ-BÁÑEZ, José Miguel, PÉREZ LANTERO, Pablo. Covering a bichromatic point set with two disjoint monochromatic disks. Computational geometry, ISSN 0925-7721. [Print ed.], 2013, vol. 46, iss. 3, str. 203-212. [COBISS-SI-ID 16326233]
CABELLO, Sergio, GIANNOPOULOS, Panos, KNAUER, Christian, MARX, Dániel, ROTE, Günter. Geometric clustering: fixed-parameter tractability and lower bounds with respect to the dimension. ACM transactions on algorithms, ISSN 1549-6325, 2011, vol. 7, no. 4, article 43 (27 str.). [COBISS-SI-ID 16028761]
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]
Emil Žagar:
JAKLIČ, Gašper, SAMPOLI, Maria Lucia, SESTINI, Alessandra, ŽAGAR, Emil. C [sup] 1 rational interpolation of spherical motions with rational rotation-minimizing directed frames. Computer Aided Geometric Design, ISSN 0167-8396, 2013, vol. 30, iss. 1, str. 159-173. [COBISS-SI-ID 16368729]
JAKLIČ, Gašper, KANDUČ, Tadej, PRAPROTNIK, Selena, ŽAGAR, Emil. Energy minimizing mountain ascent. Journal of optimization theory and applications, ISSN 0022-3239, 2012, vol. 155, is. 2, str. 680-693. ,. [COBISS-SI-ID 4382935]
JAKLIČ, Gašper, ŽAGAR, Emil. Curvature variation minimizing cubic Hermite interpolants. Applied mathematics and computation, ISSN 0096-3003. [Print ed.], 2011, vol. 218, iss. 7, str. 3918-3924. [COBISS-SI-ID 16049241]