# 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;
• rd, 3 variable reaction diffusion;
• reimer5;
• reimer6;
• rosenbrock;
• schwefel;
• smith1;
• smith2;
• virasoro;
• wright;
• zakharov;

### 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.

### Examples and Tests:

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