401-3908-21L Polynomial Optimization
Semester | Spring Semester 2021 |
Lecturers | A. A. Kurpisz |
Periodicity | non-recurring course |
Language of instruction | English |
Courses
Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|
401-3908-21 G | Polynomial Optimization | 3 hrs |
| A. A. Kurpisz |
Catalogue data
Abstract | Introduction to Polynomial Optimization and methods to solve its convex relaxations. |
Objective | The 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. |
Content | Key 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 notes | A script will be provided. |
Literature | Other 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 / Notice | Background 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 credits | 6 credits |
Examiners | A. A. Kurpisz |
Type | end-of-semester examination |
Language of examination | English |
Repetition | A repetition date will be offered in the first two weeks of the semester immediately consecutive. |
Additional information on mode of examination | Regularly 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 course | Moodle-Kurs / Moodle course |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |