SubjectsSubjects(version: 867)
Course, academic year 2019/2020
Convex optimization - NMMB409
Title: Konvexní optimalizace
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 9
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Alexandr Kazda, 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. Alexandr Kazda, Ph.D. (01.10.2019)

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

Credit is given for earning at least two thirds of points, i.e., at least 160 out of 240. Points are given for 12 sets of homework problems and 12 quizzes (10 points per piece) 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. Alexandr Kazda, Ph.D. (01.10.2019)

The final exam is oral. The requirements correspond to the syllabus and the material presented during the lectures.

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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