Lecturer(s)


Pastor Karel, doc. Mgr. Ph.D.

Dvorská Marie, Mgr.

Course content

1.The Banach algebra 2.Spectrum in the Banach algebra 3.The Fréchet, the Gâteaux derivative, strict differentiability. 4.Derivative of a composition of two functions. Mean value theorem. 5.Inverse fuction theorem. Implicit fuction theorem. 6.Convex and the Clarke subdifferential. 7.The class of functions with locally Lipschitz gradient. 8.Monotone operators. 9.Differentiability of convex functions, Asplund spaces. 10.Applications of subdifferential calculus.

Learning activities and teaching methods

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

Learning outcomes

Understand differential calculus of nonsmooth functions.
Comprehension differential calculus of nonsmooth functions.

Prerequisites

Knowledge of basic notions of functional analysis.
KMA/FA2N

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


F.H. Clarke. (1983). Optimization and nonsmooth analysis. J.Wiley New York.

J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.

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