Lecturer(s)


Tomeček Jan, doc. RNDr. Ph.D.

Machalová Jitka, RNDr. Ph.D.

Pastor Karel, doc. Mgr. Ph.D.

Course content

1. Epigraphs of functionals. 2. Lowersemicontinuity and its characterization. 3. Convex sets. 4. Convex functionals. 5. Kernels and interiors of convex sets. 6. Continuity of convex functionals. 7. The principle of automatic continuity and the uniform boundedness principle. 8. The HahnBanach theorem. 9. Subdifferentials. 10. Normal cones. 11. MoreauRockafellar's theorems. 12. Unconstrained and constrained minimization of convex functionals. 13. Generalized convexity.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 39 hours per semester
 Homework for Teaching
 10 hours per semester
 Preparation for the Course Credit
 20 hours per semester
 Preparation for the Exam
 50 hours per semester

Learning outcomes

Understand convex functions, their subdifferentials and their usage in optimization.
Comprehension Understand the basic properties of convex functions and convex sets.

Prerequisites

Knowledge of differential calculus.

Assessment methods and criteria

Oral exam, Dialog
Credit: active participation, homework solving. Exam: the student has to understand the subject and be able to prove the principal results.

Recommended literature


J. Jahn. (2004). Vector Optimization: Theory, Applications and Extensions. Springer, Berlin.

N. Hadjisawas, S. Komlósi, S. Schaible. (2005). Handbook of generalized convexity and monotonicity. Springer New York.

V. M. Aleksejev, V. M. Tichomirov, S. V. Fomin. (1991). Matematická teorie optimálních procesů. Academia, Praha.
