Convex optimization - NMMB409
Title: Konvexní optimalizace
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 9
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Michael Kompatscher, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinné
Classification: Mathematics > Algebra
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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: Michael Kompatscher, Ph.D. (29.09.2023)

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

Credit is given for scoring at least 60% on each of four sets of homework problems.

The credit for the class is necessary to sign up for the final exam.

Literature -
Last update: T_KA (30.04.2015)

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

Requirements to the exam -
Last update: Michael Kompatscher, Ph.D. (01.10.2023)

The final exam is oral. 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