polynomials


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

Polynomials include

Licensing:

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

Languages:

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

Related Data and Programs:

asa047, a Python code which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

brent, a Python code 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 code 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 code 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.

Reference:

  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:


Last modified on 08 March 2021.