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

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 MATLAB library which
minimizes a scalar function of several variables using the NelderMead 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 NelderMead 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 hyperrectangle.
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:

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:

butcher_b.m,
bounds for the butcher polynomial.

butcher_f.m,
function for the butcher polynomial.

butcher_m.m,
problem size for the butcher polynomial.

camel_b.m,
bounds for the camel polynomial.

camel_f.m,
function for the camel polynomial.

camel_m.m,
problem size for the camel polynomial.

camera_b.m,
bounds for the camera polynomial.

camera_f.m,
function for the camera polynomial.

camera_m.m,
problem size for the camera polynomial.

caprasse_b.m,
bounds for the caprasse polynomial.

caprasse_f.m,
function for the caprasse polynomial.

caprasse_m.m,
problem size for the caprasse polynomial.

cyclic5_b.m,
bounds for the cyclic5 polynomial.

cyclic5_f.m,
function for the cyclic5 polynomial.

cyclic5_m.m,
problem size for the cyclic5 polynomial.

cyclic7_b.m,
bounds for the cyclic7 polynomial.

cyclic7_f.m,
function for the cyclic7 polynomial.

cyclic7_m.m,
problem size for the cyclic7 polynomial.

cyclic8_b.m,
bounds for the cyclic8 polynomial.

cyclic8_f.m,
function for the cyclic8 polynomial.

cyclic8_m.m,
problem size for the cyclic8 polynomial.

goldstein_price_b.m,
bounds for the goldstein_price polynomial.

goldstein_price_f.m,
function for the goldstein_price polynomial.

goldstein_price_m.m,
problem size for the goldstein_price polynomial.

hairer_b.m,
bounds for the hairer polynomial.

hairer_f.m,
function for the hairer polynomial.

hairer_m.m,
problem size for the hairer polynomial.

heart_b.m,
bounds for the heart dipole polynomial.

heart_f.m,
function for the heart dipole polynomial.

heart_m.m,
problem size for the heart dipole polynomial.

himmelblau_b.m,
bounds for the himmelblau polynomial.

himmelblau_f.m,
function for the himmelblau polynomial.

himmelblau_m.m,
problem size for the himmelblau polynomial.

hunecke_b.m,
bounds for the hunecke polynomial.

hunecke_f.m,
function for the hunecke polynomial.

hunecke_m.m,
problem size for the hunecke polynomial.

kearfott_b.m,
bounds for the kearfott polynomial.

kearfott_f.m,
function for the kearfott polynomial.

kearfott_m.m,
problem size for the kearfott polynomial.

lv3_b.m,
bounds for the adaptive LotkaVolterra 3 polynomial.

lv3_f.m,
function for the adaptive LotkaVolterra 3 polynomial.

lv3_m.m,
problem size for the adaptive LotkaVolterra 3 polynomial.

lv4_b.m,
bounds for the adaptive LotkaVolterra 4 polynomial.

lv4_f.m,
function for the adaptive LotkaVolterra 4 polynomial.

lv4_m.m,
problem size for the adaptive LotkaVolterra 4 polynomial.

magnetism6_b.m,
bounds for the magnetism6 polynomial.

magnetism6_f.m,
function for the magnetism6 polynomial.

magnetism6_m.m,
problem size for the magnetism6 polynomial.

magnetism7_b.m,
bounds for the magnetism7 polynomial.

magnetism7_f.m,
function for the magnetism7 polynomial.

magnetism7_m.m,
problem size for the magnetism7 polynomial.

quadratic_b.m,
bounds for the quadratic polynomial.

quadratic_f.m,
function for the quadratic polynomial.

quadratic_m.m,
problem size for the quadratic polynomial.

r9mat_uniform_abvec.m,
returns a matrix of N samples in an M dimensional space with
separate limits for each dimensions.

rd_b.m,
bounds for the 3 variable reaction diffusion polynomial.

rd_f.m,
function for the 3 variable reaction diffusion polynomial.

rd_m.m,
problem size for the 3 variable reaction diffusion polynomial.

reimer5_b.m,
bounds for the reimer5 polynomial.

reimer5_f.m,
function for the reimer5 polynomial.

reimer5_m.m,
problem size for the reimer5 polynomial.

reimer6_b.m,
bounds for the reimer6 polynomial.

reimer6_f.m,
function for the reimer6 polynomial.

reimer6_m.m,
problem size for the reimer6 polynomial.

rosenbrock_b.m,
bounds for the rosenbrock polynomial.

rosenbrock_f.m,
function for the rosenbrock polynomial.

rosenbrock_m.m,
problem size for the rosenbrock polynomial.

schwefel_b.m,
bounds for the schwefel polynomial.

schwefel_f.m,
function for the schwefel polynomial.

schwefel_m.m,
problem size for the schwefel polynomial.

smith1_b.m,
bounds for the smith1 polynomial.

smith1_f.m,
function for the smith1 polynomial.

smith1_m.m,
problem size for the smith1 polynomial.

smith2_b.m,
bounds for the smith2 polynomial.

smith2_f.m,
function for the smith2 polynomial.

smith2_m.m,
problem size for the smith2 polynomial.

timestamp.m,
prints the current YMDHMS date as a time stamp.

virasoro_b.m,
bounds for the virasoro polynomial.

virasoro_f.m,
function for the virasoro polynomial.

virasoro_m.m,
problem size for the virasoro polynomial.

wright_b.m,
bounds for the wright polynomial.

wright_f.m,
function for the wright polynomial.

wright_m.m,
problem size for the wright polynomial.

zakharov_b.m,
bounds for the zakharov polynomial.

zakharov_f.m,
function for the zakharov polynomial.

zakharov_m.m,
problem size for the zakharov polynomial.
Examples and Tests:
You can go up one level to
the MATLAB source codes.
Last modified on 26 January 2016.