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

butcher;

camel;

camera;

caprasse;

cyclic5;

cyclic7;

cyclic8;

goldstein_price;

hairer;

heart, heart dipole;

himmelblau;

hunecke;

kearfott;

lv3, adaptive LotkaVolterra 3 system;

lv4, adaptive LotkaVolterra 4 system;

magnetism6;

magnetism7;

quadratic;

rd, 3 variable reaction diffusion;

reimer5;

reimer6;

rosenbrock;

schwefel;

smith1;

smith2;

virasoro;

wright;

zakharov;
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 Python code which
minimizes a scalar function of several variables
using the NelderMead 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 HookeJeeves method, by Arthur Kaupe.
This is a version of ACM TOMS algorithm 178.
Reference:

Cesar Munoz, Anthony Narkawicz,
Formalization of Bernstein polynomials and applications to global
optimization,
Journal of Automated Reasoning,
Volume 51, Number 2, 2013, pages 151196.

Sashwati Ray, PSV Nataraj,
An efficient algorithm for range computation of polynomials using the
Bernstein form,
Journal of Global Optimization,
Volume 45, 2009, pages 403426.

Andrew Smith,
Fast construction of constant bound functions for sparse polynomials,
Journal of Global Optimization,
Volume 43, 2009, pages 445458.

Jan Verschelde,
PHCPACK: A generalpurpose solver for polynomial systems by
homotopy continuation,
ACM Transactions on Mathematical Software,
Volume 25, Number 2, June 1999, pages 251276.
Source Code:
Last modified on 08 March 2021.