POEM – Effective Methods in Polynomial Optimization

POEM is a software for solving polynomial optimization problems developed at the Applied Algebra group at the Institute for Analysis and Algebra at Technische Universität Braunschweig.
It mainly uses sums of nonnegative circuit polynomials (SONC), a certificate for nonnegativity of polynomials independent of sums of squares, which were developed by Timo de Wolff and Sadik Iliman. SONC certificates are computed via geometric programs. POEM can also compute solutions via SAGE (sums of AM-GM exponentials) and SOS (sums of squares) certificates. POEM uses a variety of established solvers. It is written in Python.


Please note that this software is a prototype and an alpha version. As such it is preliminary, released for test-purposes only, and subject to change without notice.

Although the code was tested with multiple instances, it may still contain errors, bugs, or an offensive coding style. There is no warranty, not even for merchantability or fitness for a particular purpose.


Current Team

Timo de Wolff, Janin Heuer and Helena Müller (ZIB).

Feedback, suggestions, and bug reports are very welcome; please contact us via email: Timo, Janin.

For planed new content, and content in development see the Upcoming Features.

Past Team Members

Henning Seidler.


The Software is published under GNU public license.

Citing POEM

If you find POEM useful, you can cite it using the following BibTex entry.

  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version},
  Author       = {Seidler, Henning and de Wolff, Timo},
  HowPublished = {\url{http://www.iaa.tu-bs.de/AppliedAlgebra/POEM/index.html}},
  Month        = {jul},
  Year         = {2019}


This work was supported by the Deutsche Forschungsgemeinschaft via the DFG grant WO 2206/1-1 (PI: Timo de Wolff).

Last Update: April 07, 2020