POEM – History

To comply with our ChangeLog on gitlab, we present the versions and their changes in chronological order.

Version 0.1.0.0

Date: 2018-02-12

Features:

• Read polynomials from string, as matrix/vector-pair or generate new random instances.
• Compute lower bounds for unconstraint polynomial minimization problems via various methods:
  • SONC, using cvxpy and ECOS/SCS in Python
  • SONC, using cvx and SeDuMi/SDPT3 in Matlab
  • SOS, using cvxpy and SCS in Python
  • SOS, using cvx and SeDuMi/SDPT3 in Matlab
  • SOS, using SOStools in Matlab
  • SOS, using Gloptipoly in Matlab
• all methods are accessed via a Python interface.
• obtain the decomposition into non-negative polynomials (see Known Issues).

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.1.0.0},
	  Author       = {Seidler, Henning and de Wolff, Timo},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {feb},
	  Year         = {2018}
	}
				

Version 0.1.1.0

Date: 2018-07-24

Added Features:

• Coefficients for solution written in sparse matrix/tensor
• First Version for reallocation of coefficients for negative points
• Greatly reduced number of variables in big GP

Fixed Issues

• Decomposition for SONC works in all cases

Known Issues

• Decomposition into squares will fail, if Gloptipoly/SOStools do not return a full-sized matrix, i.e. if some monomials do not appear in the solution.
• Reallocation of coefficients often fails, since ECOS tends to fail after some iterations

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.1.1.0},
	  Author       = {Seidler, Henning and de Wolff, Timo},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {jul},
	  Year         = {2018}
	}
				

Version 0.1.1.1

Date: 2019-01-11

Fixed Issues

• Adjusted syntax for new versions of cvxpy and sympy

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.1.1.1},
	  Author       = {Seidler, Henning and de Wolff, Timo},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {jan},
	  Year         = {2019}
	}
				

Version 0.2.0.0

Date: 2019-01-30

Added Features:

• Computer lower bounds via SAGE
• Obtain rational lower bound in exact arithmetic; and decomposition with rational coefficients in exact arithmetic, both via SONC and SAGE
• Compute local minimizers

Notable Changes

• Function calls for SONC unified
• separate class polynomial_base for input/output
• own classes for AGE- and circuit-polynomials

Known Issues

• Matlab currently not available, was not tested in a while, may become deprecated
• Decomposition for SOS will fail, if psd-matrix does not have full size, i.e. if some monomials do not appear in the solution.
• Symbolic decomposition of SAGE fails in many instances

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.2.0.0},
	  Author       = {Seidler, Henning and de Wolff, Timo},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {jan},
	  Year         = {2019}
	}
				

Version 0.2.0.1

Date: 2019-02-14

Fixed Issues

• Some imports were missing in setup.py.
• When reading from string (or database), coefficients alsways had type "object".
• In detect_infinity, reduced digits for rounding from 23 to 7 (error happened, when going from decimal to binary).

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.2.0.1},
	  Author       = {Seidler, Henning and de Wolff, Timo},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {feb},
	  Year         = {2019}
	}
				

Version 0.2.1.0

Date: 2019-07-04

Added Features:

• Divided required packages into minimal/standard/full
• Additional flags for setup
• Compute minimiser of a Circuit Polynomial
• SONC/SAGE solvable with MOSEK 9
• Check nonnegativity exactly with Z3

Other Changes

• Use cdd as default solver for exact LP.
• rename Polynomial.symbolic() -> Polynomial.to_symbolic()

Fixed Issues

• Specified Exceptions
• Changed some objects from numpy.matrix to numpy.array
• Added missing docstrings
• Removing some unused imports

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.2.1.0},
	  Author       = {Seidler, Henning and de Wolff, Timo},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {jul},
	  Year         = {2019}
	}
				

Version 0.3.0.0

Date: 2021-05-27

Added Features:

• Improved Lower Bounds via branch-and-bound
• alternative approach by running orthants in parallel

Other Changes

• removed SONC optimisation in Matlab
• removed dependency of polymake, directly uses cddlib
• aux.py has type annotations

Fixed Issues

• Additional error handling
• Fixed Matlab bridge
• Clean-up of files

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.3.0.0},
	  Author       = {Seidler, Henning},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {may},
	  Year         = {2021}
	}
				

Version 0.3.0.1

Date: 2021-08-25

Fixed Issues

• fixed example in Readme
• handle MatlabError

Citing:

	@Misc{poem:software,
	  Title        = {{POEM}: Effective Methods in Polynomial Optimization, version 0.3.0.1},
	  Author       = {Seidler, Henning},
	  HowPublished = {\url{http://www.user.tu-berlin.de/henning.seidler/POEM/}},
	  Month        = {aug},
	  Year         = {2021}
	}
				

Last Update: May 5, 2022