POLYNOMIALS
Polynomials for Global Optimization Tests


POLYNOMIALS is a MATLAB 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

Licensing:

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

Languages:

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

Related Data and Programs:

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

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

ENTRUST, a MATLAB program which minimizes a scalar function of several variables using trust region methods.

NELDER_MEAD, a MATLAB program which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

TEST_OPT, a MATLAB library which defines test problems for the minimization of a scalar function of several variables.

TEST_OPT_CON, a MATLAB library which defines test problems for the minimization of a scalar function of several variables, with the search constrained to lie within a specified hyper-rectangle.

TEST_OPTIMIZATION, a MATLAB library which defines test problems for the minimization of a scalar function of several variables, as described by Molga and Smutnicki.

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:

Examples and Tests:

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


Last modified on 26 January 2016.