POLYNOMIALS
Polynomials for Global Optimization Tests

POLYNOMIALS is a FORTRAN90 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 FORTRAN90 library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

BRENT, a FORTRAN90 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 FORTRAN90 library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

TEST_OPT, a FORTRAN90 library which defines test problems for the minimization of a scalar function of several variables.

TEST_OPT_CON, a FORTRAN90 library 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, a FORTRAN90 library which defines test problems for the minimization of a scalar function of several variables, as described by Molga and Smutnicki.

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:

• polynomials.f90, the source code.

Examples and Tests:

• polynomials_test.f90, a sample calling program.
• polynomials_test.txt, the output file.

List of Routines:

• BUTCHER_B returns the bounds in the butcher problem.
• BUTCHER_F returns the function in the butcher problem.
• BUTCHER_M returns the number of variables in the butcher problem.
• CAMEL_B returns the bounds in the camel problem.
• CAMEL_F returns the function in the camel problem.
• CAMEL_M returns the number of variables in the camel problem.
• CAMERA_B returns the bounds in the camera problem.
• CAMERA_F returns the function in the camera problem.
• CAMERA_M returns the number of variables in the camera problem.
• CAPRASSE_B returns the bounds in the caprasse problem.
• CAPRASSE_F returns the function in the caprasse problem.
• CAPRASSE_M returns the number of variables in the caprasse problem.
• CYCLIC5_B returns the bounds in the cyclic5 problem.
• CYCLIC5_F returns the function in the cyclic5 problem.
• CYCLIC5_M returns the number of variables in the cyclic5 problem.
• CYCLIC7_B returns the bounds in the cyclic7 problem.
• CYCLIC7_F returns the function in the cyclic7 problem.
• CYCLIC7_M returns the number of variables in the cyclic7 problem.
• CYCLIC8_B returns the bounds in the cyclic8 problem.
• CYCLIC8_F returns the function in the cyclic8 problem.
• CYCLIC8_M returns the number of variables in the cyclic8 problem.
• GOLDSTEIN_PRICE_B returns the bounds in the goldstein_price problem.
• GOLDSTEIN_PRICE_F returns the function in the goldstein_price problem.
• GOLDSTEIN_PRICE_M returns the number of variables in the goldstein_price problem.
• HAIRER_B returns the bounds in the hairer problem.
• HAIRER_F returns the function in the hairer problem.
• HAIRER_M returns the number of variables in the hairer problem.
• HEART_B returns the bounds in the heart problem.
• HEART_F returns the function in the heart problem.
• HEART_M returns the number of variables in the heart problem.
• HIMMELBLAU_B returns the bounds in the himmelblau problem.
• HIMMELBLAU_F returns the function in the himmelblau problem.
• HIMMELBLAU_M returns the number of variables in the himmelblau problem.
• HUNECKE_B returns the bounds in the hunecke problem.
• HUNECKE_F returns the function in the hunecke problem.
• HUNECKE_M returns the number of variables in the hunecke problem.
• KEARFOTT_B returns the bounds in the kearfott problem.
• KEARFOTT_F returns the function in the kearfott problem.
• KEARFOTT_M returns the number of variables in the kearfott problem.
• LV3_B returns the bounds in the lv3 problem.
• LV3_F returns the function in the lv3 problem.
• LV3_M returns the number of variables in the lv3 problem.
• LV4_B returns the bounds in the lv4 problem.
• LV4_F returns the function in the lv4 problem.
• LV4_M returns the number of variables in the lv4 problem.
• MAGNETISM6_B returns the bounds in the magnetism6 problem.
• MAGNETISM6_F returns the function in the magnetism6 problem.
• MAGNETISM6_M returns the number of variables in the magnetism6 problem.
• MAGNETISM7_B returns the bounds in the magnetism7 problem.
• MAGNETISM7_F returns the function in the magnetism7 problem.
• MAGNETISM7_M returns the number of variables in the magnetism7 problem.
• QUADRATIC_B returns the bounds in the quadratic problem.
• QUADRATIC_F returns the function in the quadratic problem.
• QUADRATIC_M returns the number of variables in the quadratic problem.
• R8MAT_UNIFORM_ABVEC returns a scaled pseudorandom R8MAT.
• RD_B returns the bounds in the rd problem.
• RD_F returns the function in the rd problem.
• RD_M returns the number of variables in the rd problem.
• REIMER5_B returns the bounds in the reimer5 problem.
• REIMER5_F returns the function in the reimer5 problem.
• REIMER5_M returns the number of variables in the reimer5 problem.
• REIMER6_B returns the bounds in the reimer6 problem.
• REIMER6_F returns the function in the reimer6 problem.
• REIMER6_M returns the number of variables in the reimer6 problem.
• ROSENBROCK_B returns the bounds in the rosenbrock problem.
• ROSENBROCK_F returns the function in the rosenbrock problem.
• ROSENBROCK_M returns the number of variables in the rosenbrock problem.
• SCHWEFEL_B returns the bounds in the schwefel problem.
• SCHWEFEL_F returns the function in the schwefel problem.
• SCHWEFEL_M returns the number of variables in the schwefel problem.
• SMITH1_B returns the bounds in the smith1 problem.
• SMITH1_F returns the function in the smith1 problem.
• SMITH1_M returns the number of variables in the smith1 problem.
• SMITH2_B returns the bounds in the smith2 problem.
• SMITH2_F returns the function in the smith2 problem.
• SMITH2_M returns the number of variables in the smith2 problem.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• VIRASORO_B returns the bounds in the virasoro problem.
• VIRASORO_F returns the function in the virasoro problem.
• VIRASORO_M returns the number of variables in the virasoro problem.
• WRIGHT_B returns the bounds in the wright problem.
• WRIGHT_F returns the function in the wright problem.
• WRIGHT_M returns the number of variables in the wright problem.
• ZAKHAROV_B returns the bounds in the zakharov problem.
• ZAKHAROV_F returns the function in the zakharov problem.
• ZAKHAROV_M returns the number of variables in the zakharov problem.

You can go up one level to the FORTRAN90 source codes.