POLYNOMIALS
Polynomials for Global Optimization Tests

POLYNOMIALS is a Python 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 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 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 library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

BRENT, a Python 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 Python library 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 library 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:

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:

• butcher.py, the butcher polynomial.
• camel.py, the camel polynomial.
• camera.py, the camera polynomial.
• caprasse.py, the caprasse polynomial.
• cyclic5.py, the cyclic5 polynomial.
• cyclic7.py, the cyclic7 polynomial.
• cyclic8.py, the cyclic8 polynomial.
• goldstein_price.py, the goldstein_price polynomial.
• hairer.py, the hairer polynomial.
• heart.py, the heart dipole polynomial.
• himmelblau.py, the himmelblau polynomial.
• hunecke.py, the hunecke polynomial.
• kearfott.py, the kearfott polynomial.
• lv3.py, the adaptive Lotka-Volterra 3 polynomial.
• lv4.py, the adaptive Lotka-Volterra 4 polynomial.
• magnetism6.py, the magnetism6 polynomial.
• magnetism7.py, the magnetism7 polynomial.
• quadratic.py, 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.py, the 3 variable reaction diffusion polynomial.
• reimer5.py, the reimer5 polynomial.
• reimer6.py, the reimer6 polynomial.
• rosenbrock.py, the rosenbrock polynomial.
• schwefel.py, the schwefel polynomial.
• smith1.py, the smith1 polynomial.
• smith2.py, the smith2 polynomial.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• virasoro.py, the virasoro polynomial.
• wright.py, the wright polynomial.
• zakharov.py, the zakharov polynomial.

Examples and Tests:

• polynomials.py, calls all the tests;
• polynomials.txt, the output file.

You can go up one level to the Python source codes.