401-3908-21L  Polynomial Optimization

SemesterSpring Semester 2021
LecturersA. A. Kurpisz
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3908-21 GPolynomial Optimization3 hrs
Wed16:15-18:00HG F 5 »
Fri13:15-14:00HG E 1.2 »
A. A. Kurpisz

Catalogue data

AbstractIntroduction to Polynomial Optimization and methods to solve its convex relaxations.
ObjectiveThe goal of this course is to provide a treatment of non-convex Polynomial Optimization problems through the lens of various techniques to solve its convex relaxations. Part of the course will be focused on learning how to apply these techniques to practical examples in finance, robotics and control.
ContentKey topics include:
- Polynomial Optimization as a non-convex optimization problem and its connection to certifying non-negativity of polynomials
- Optimization-free and Linear Programming based techniques to approach Polynomial Optimization problems.
- Introduction of Second-Order Cone Programming, Semidefinite Programming and Relative Entropy Programming as a tool to solve relaxations of Polynomial Optimization problems.
- Applications to optimization problems in finance, robotics and control.
Lecture notesA script will be provided.
LiteratureOther helpful materials include:
- Jean Bernard Lasserre, An Introduction to Polynomial and Semi-Algebraic Optimization, Cambridge University Press, February 2015
- Pablo Parrilo. 6.972 Algebraic Techniques and Semidefinite Optimization. Spring 2006. Massachusetts Institute of Technology: MIT OpenCourseWare, . License: .
Prerequisites / NoticeBackground in Linear and Integer Programming is recommended.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 credits
ExaminersA. A. Kurpisz
Typeend-of-semester examination
Language of examinationEnglish
RepetitionA repetition date will be offered in the first two weeks of the semester immediately consecutive.
Additional information on mode of examinationRegularly during the course various exercises will be published in advance and solutions will be presented during the lectures. Students will have an opportunity to voluntarily present their solutions during the lectures. Such activity will be rewarded with extra points that can increase the final grade by up to 0.25.

Mode of the end-of-semester examination: written 180 minutes.
Written aids: None.

Learning materials

 
Moodle courseMoodle-Kurs / Moodle course
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics BachelorSelection: Mathematical Optimization, Discrete MathematicsWInformation
Mathematics MasterSelection: Mathematical Optimization, Discrete MathematicsWInformation
Computational Science and Engineering BachelorElectivesWInformation
Computational Science and Engineering MasterElectivesWInformation