Convex sets and functions, convex programming. Lagrange duality, dual problem, weak and strong duality. Slater's condition, the Karush-Kuhn-Tucker theorem.

Linearly constrained optimization problems, quadratic and semidefinite programming with generalizations. Numerical procedures, penalty functions. Integer programming.A short overview of software tools for solving optimization problems.

# Optimization 2

S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge Univ. Press, Cambridge, 2004.

B. H. Korte, J. Vygen: Combinatorial Optimization: Theory and Algorithms, 3. izdaja, Springer, Berlin, 2006.

Students encounter the fundamental types of problems in mathematical programming, with emphasis on the convex ones. They get to know the basic mathematical tools for tackling these problems, using appropriate software packages for solving them in practice.

Knowledge and understanding: Students are able to model various important applied problems accurately. They are familiar with the basic techniques and software tools that can be used to solve the resulting optimization problems efficiently.Application: Solving optimization problems which appear in practice.Reflection: The importance of representing practical problems in a formal way which helps to solve them efficiently and adequately.Transferable skills: Ability to model practical problems as mathematically formulated optimization problems, to distinguish between computationally feasible and infeasible problems, to construct models on one's own and to analyze them by means of appropriate software tools.

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

Type (examination, oral, coursework, project):

2 midterm exams instead of written exam, written exam

oral exam

Grading: 1-5 (fail), 6-10 (pass) (according to the Statute of UL)

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]