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401-3908-21L 6 Credits BSC , DR , MSC D-MATH

Polynomial Optimization

Lecturers & Examiners: Dr. Adam Andrzej Kurpisz

VVZ CR n/a

Last Updated: 2026-02-05 15:54:11

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.

Resources

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: .

Learning Materials (Links)

Moodle course
Moodle-Kurs / Moodle course

General Information

Language: English
Levels: BSC , DR , MSC

Examination

Type: end-of-semester 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.

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Polynomial Optimization	Wed 16:15-18:00 (HG F 5) Fri 13:15-14:00 (HG E 1.2)	3 h weekly

Offered In

Mathematics Bachelor
- Electives
  - Selection: Mathematical Optimization, Discrete Mathematics
Computational Science and Engineering Bachelor
- For All Programme Regulations
  - Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
Computational Science and Engineering Master
- Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
Mathematics Master
- Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Electives: Applied Mathematics and Further Application-Oriented Fields (¬)
    - Selection: Mathematical Optimization, Discrete Mathematics
Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)
- Graduate School (Official website of the Zurich Graduate School in Mathematics:)