Polynomials for Global Optimization Tests

POLYNOMIALS is a Python library which defines multivariate polynomials over rectangular domains, for which certain information is to be determined, such as the maximum and minimum values.

Polynomials include


The computer code and data files made available on this web page are distributed under the GNU LGPL license.


POLYNOMIALS is available in a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ASA047, a Python library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

BRENT, a Python library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.

COMPASS_SEARCH, a Python library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

TOMS178, a Python library which optimizes a scalar functional of multiple variables using the Hooke-Jeeves method, by Arthur Kaupe. This is a version of ACM TOMS algorithm 178.


  1. Cesar Munoz, Anthony Narkawicz,
    Formalization of Bernstein polynomials and applications to global optimization,
    Journal of Automated Reasoning,
    Volume 51, Number 2, 2013, pages 151-196.
  2. Sashwati Ray, PSV Nataraj,
    An efficient algorithm for range computation of polynomials using the Bernstein form,
    Journal of Global Optimization,
    Volume 45, 2009, pages 403-426.
  3. Andrew Smith,
    Fast construction of constant bound functions for sparse polynomials,
    Journal of Global Optimization,
    Volume 43, 2009, pages 445-458.
  4. Jan Verschelde,
    PHCPACK: A general-purpose solver for polynomial systems by homotopy continuation,
    ACM Transactions on Mathematical Software,
    Volume 25, Number 2, June 1999, pages 251-276.

Source Code:

Examples and Tests:

You can go up one level to the Python source codes.

Last modified on 06 December 2016.