polynomials


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

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

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

polynomials_test

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

test_opt_con, a MATLAB code 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 code 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:


Last modified on 27 February 2019.