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 Lotka-Volterra 3 system;
-
lv4, adaptive Lotka-Volterra 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 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:
-
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.
-
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.
-
Andrew Smith,
Fast construction of constant bound functions for sparse polynomials,
Journal of Global Optimization,
Volume 43, 2009, pages 445-458.
-
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.