Optimization methods 2

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

Semirings and shortest path problem.
Hard problems of combinatorial optimization.
Integer optimization problems.
Interior point methods.
Calculus of variations.
Software tools for optimization.
Applications of optimization.

Readings

S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge University Press, Cambridge, 2004.
B. van Brunt: The calculus of variations. Springer, Berlin, 2004.
B. H. Korte, J. Vygen: Combinatorial Optimization: Theory and Algorithms, 4. izdaja, Springer, Berlin, 2008.
D. Li, X. Sun: Nonlinear integer programming. Springer, Berlin, 2006.
Z. Michalewicz, D. B. Fogel: How to Solve It: Modern Heuristics, 2. izdaja, Springer, Berlin, 2004.
P. Pablo Pedregal: Introduction to optimization, Springer, Berlin, 2004.
A. Schrijver: Combinatorial optimization, Springer, Berlin, 2004.
M. Gendreau, J-Y. Potvin: Handbook of Metaheuristics. Springer, 2010.

Objectives and competences

The goal of the course is to introduce some modern optimization methods and to enable the students to use these methods by themselves in solving practical problems.

Intended learning outcomes

Knowledge and understanding:
Understanding of concepts and methods for solving the selected types of optimization problems.
Ability to select the right optimization methods and perform them using appropriate software tools.
Mathematical modeling of practical problems.

Learning and teaching methods

Lectures, seminar, exercises, homeworks, home reading, project, consultations, independent work by the students.

Assessment

Type (examination, oral, coursework, project):

Continuous assessment (homework, midterm exams, project work)
Final (written or oral exam)

Grading: 6-10 pass, 5 fail (according to the rules of University of Ljubljana)

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]