polynomials
polynomials,
an Octave 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
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butcher;
-
camel;
-
camera;
-
caprasse;
-
cyclic5;
-
cyclic7;
-
cyclic8;
-
goldstein_price;
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hairer;
-
heart, heart dipole;
-
himmelblau;
-
hunecke;
-
kearfott;
-
lv3, adaptive Lotka-Volterra 3 system;
-
lv4, adaptive Lotka-Volterra 4 system;
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magnetism6;
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magnetism7;
-
quadratic;
-
rd, 3 variable reaction diffusion;
-
reimer5;
-
reimer6;
-
rosenbrock;
-
schwefel;
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smith1;
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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
an Octave version and
a Python version.
Related Data and Programs:
polynomials_test
asa047,
an Octave code which
minimizes a scalar function of several variables using
the Nelder-Mead algorithm.
compass_search,
an Octave 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,
an Octave code which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
test_opt,
an Octave code which
defines test problems for the minimization of a scalar function
of several variables.
test_opt_con,
an Octave 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,
an Octave code 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 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:
-
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.
-
butcher_max_fun.m,
butcher polynomial function for fmincon maximization.
-
butcher_min_fun.m,
butcher polynomial function for fmincon minimization.
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camel_b.m,
bounds for the camel polynomial.
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camel_f.m,
function for the camel polynomial.
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camel_m.m,
problem size for the camel polynomial.
-
camera_b.m,
bounds for the camera polynomial.
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camera_f.m,
function for the camera polynomial.
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camera_m.m,
problem size for the camera polynomial.
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caprasse_b.m,
bounds for the caprasse polynomial.
-
caprasse_f.m,
function for the caprasse polynomial.
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caprasse_m.m,
problem size for the caprasse polynomial.
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cyclic5_b.m,
bounds for the cyclic5 polynomial.
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cyclic5_f.m,
function for the cyclic5 polynomial.
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cyclic5_m.m,
problem size for the cyclic5 polynomial.
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cyclic7_b.m,
bounds for the cyclic7 polynomial.
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cyclic7_f.m,
function for the cyclic7 polynomial.
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cyclic7_m.m,
problem size for the cyclic7 polynomial.
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cyclic8_b.m,
bounds for the cyclic8 polynomial.
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cyclic8_f.m,
function for the cyclic8 polynomial.
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cyclic8_m.m,
problem size for the cyclic8 polynomial.
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goldstein_price_b.m,
bounds for the goldstein_price polynomial.
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goldstein_price_f.m,
function for the goldstein_price polynomial.
-
goldstein_price_m.m,
problem size for the goldstein_price polynomial.
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hairer_b.m,
bounds for the hairer polynomial.
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hairer_f.m,
function for the hairer polynomial.
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hairer_m.m,
problem size for the hairer polynomial.
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heart_b.m,
bounds for the heart dipole polynomial.
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heart_f.m,
function for the heart dipole polynomial.
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heart_m.m,
problem size for the heart dipole polynomial.
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himmelblau_b.m,
bounds for the himmelblau polynomial.
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himmelblau_f.m,
function for the himmelblau polynomial.
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himmelblau_m.m,
problem size for the himmelblau polynomial.
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hunecke_b.m,
bounds for the hunecke polynomial.
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hunecke_f.m,
function for the hunecke polynomial.
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hunecke_m.m,
problem size for the hunecke polynomial.
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kearfott_b.m,
bounds for the kearfott polynomial.
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kearfott_f.m,
function for the kearfott polynomial.
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kearfott_m.m,
problem size for the kearfott polynomial.
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lv3_b.m,
bounds for the adaptive Lotka-Volterra 3 polynomial.
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lv3_f.m,
function for the adaptive Lotka-Volterra 3 polynomial.
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lv3_m.m,
problem size for the adaptive Lotka-Volterra 3 polynomial.
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lv4_b.m,
bounds for the adaptive Lotka-Volterra 4 polynomial.
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lv4_f.m,
function for the adaptive Lotka-Volterra 4 polynomial.
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lv4_m.m,
problem size for the adaptive Lotka-Volterra 4 polynomial.
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magnetism6_b.m,
bounds for the magnetism6 polynomial.
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magnetism6_f.m,
function for the magnetism6 polynomial.
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magnetism6_m.m,
problem size for the magnetism6 polynomial.
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magnetism7_b.m,
bounds for the magnetism7 polynomial.
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magnetism7_f.m,
function for the magnetism7 polynomial.
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magnetism7_m.m,
problem size for the magnetism7 polynomial.
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quadratic_b.m,
bounds for the quadratic polynomial.
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quadratic_f.m,
function for the quadratic polynomial.
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quadratic_m.m,
problem size for the quadratic polynomial.
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r9mat_uniform_abvec.m,
returns a matrix of N samples in an M dimensional space with
separate limits for each dimensions.
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rd_b.m,
bounds for the 3 variable reaction diffusion polynomial.
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rd_f.m,
function for the 3 variable reaction diffusion polynomial.
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rd_m.m,
problem size for the 3 variable reaction diffusion polynomial.
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reimer5_b.m,
bounds for the reimer5 polynomial.
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reimer5_f.m,
function for the reimer5 polynomial.
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reimer5_m.m,
problem size for the reimer5 polynomial.
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reimer6_b.m,
bounds for the reimer6 polynomial.
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reimer6_f.m,
function for the reimer6 polynomial.
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reimer6_m.m,
problem size for the reimer6 polynomial.
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rosenbrock_b.m,
bounds for the rosenbrock polynomial.
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rosenbrock_f.m,
function for the rosenbrock polynomial.
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rosenbrock_m.m,
problem size for the rosenbrock polynomial.
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schwefel_b.m,
bounds for the schwefel polynomial.
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schwefel_f.m,
function for the schwefel polynomial.
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schwefel_m.m,
problem size for the schwefel polynomial.
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smith1_b.m,
bounds for the smith1 polynomial.
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smith1_f.m,
function for the smith1 polynomial.
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smith1_m.m,
problem size for the smith1 polynomial.
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smith2_b.m,
bounds for the smith2 polynomial.
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smith2_f.m,
function for the smith2 polynomial.
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smith2_m.m,
problem size for the smith2 polynomial.
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virasoro_b.m,
bounds for the virasoro polynomial.
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virasoro_f.m,
function for the virasoro polynomial.
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virasoro_m.m,
problem size for the virasoro polynomial.
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wright_b.m,
bounds for the wright polynomial.
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wright_f.m,
function for the wright polynomial.
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wright_m.m,
problem size for the wright polynomial.
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zakharov_b.m,
bounds for the zakharov polynomial.
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zakharov_f.m,
function for the zakharov polynomial.
-
zakharov_m.m,
problem size for the zakharov polynomial.
Last modified on 25 April 2023.