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Course, academic year 2022/2023
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Convex optimization - NMMB409
Title: Konvexní optimalizace
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 9
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Zuzana Patáková, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinné
Classification: Mathematics > Algebra
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.05.2018)
Compulsory course for the programme Mathematics for Information Technologies.
Course completion requirements -
Last update: RNDr. Zuzana Patáková, Ph.D. (29.09.2022)

To finish the course a student needs to gain credit ("zápočet") and then pass the final exam.

Credit is given for earning at least 77 points out of 128. Points are given for 4 sets of homework problems (20 points per piece), 12 online quizzed (2 points per piece) and activity during tutorials (2 points per session) that will be assigned throughout the semester.

Credit for the class is necessary to sign up for the final exam. The nature of the credit (numerous small assignments during the whole semester) does not allow a repeat attempt at gaining credit for the course.

Literature -
Last update: T_KA (30.04.2015)

S. Boyd, L. Vandengerghe, Convex Optimization, Cambridge University Press 2004,

Requirements to the exam -
Last update: RNDr. Zuzana Patáková, Ph.D. (07.09.2022)

The final exam consists of a written test and an oral examination. The requirements correspond to the syllabus and the material presented during the lectures. It is necessary to first gain credit ("zápočet") before signing up for the final exam.

Syllabus -
Last update: RNDr. Alexandr Kazda, Ph.D. (01.10.2019)

1. Convex and affine sets, their properties

2. Convex functions, their properties, quasiconvex functions

3. Convex optimization problems, convex optimization, linear optimization, quadratic optimization, geometric programming, vector optimization

4. Duality, Lagrange dual function, Lagrange dual problem, geometric interpretation, perturbation and sensitivity analysis

5. Applications in approximation and data processing

6. Geometric applications, Support Vector Machines

7. Statistical applications (maximum likelihood method, MAP)

8. Algorithms for minimization without constraints or with constraints in the form of equalities

9. Interior point methods

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