# test_opt_con

test_opt_con, a FORTRAN90 code which defines a set of constrained global optimization problems.

A typical constrained global optimization problem presents an M-dimensional hyper-rectangle bounded by A(1:M) <= X(1:M) <= B(1:M), and a scalar-valued function F(X). The task is to find a point X within the hyper-rectangle at which the function takes its minimum value.

This task is impossible, mathematically and in general. However, the problems that can be solved mathematically are often not the ones encountered in real life. Thus, it is useful to try to solve an impossible problem, since an approximate answer to such a problem can be all we can hope for or need.

The functions defined include:

1. NM1: Niederreiter-McCurley function #1, M = 4;
2. NM2: Niederreiter-McCurley function #2, M = 4;
3. NM3: Niederreiter-McCurley function #3, M = 4;
4. NM4: Niederreiter-McCurley function #4, M = 4;
5. NM5: Niederreiter-McCurley function #5, M = 4;
6. NM6: Niederreiter-McCurley function #6, M = 4;
7. NM6: Niederreiter-McCurley function #6, M = 4;
8. L02: Langerman function, M = 2;
9. L10: Langerman function, M = 10;

For each function, the library includes a routine to evaluate the function, but also routines to return the limits of the hyper-rectangle, the spatial dimension, the solution, if known, and a title for the problem. These routines have a standard set of names based on the function index. For instance, for function #3, we have the routines:

• P03_AB returns bounds for problem 3.
• P03_F returns the objective function value for problem 3.
• P03_M returns the spatial dimension for problem 3.
• P03_SOL returns known solutions for problem 3.
• P03_TITLE returns a title for problem 3.

Since the same interface is used for each function, if you wish to work with problem 6 instead, you simply change the "03" to "06" in your routine calls.

If you wish to call all of the functions, you can write a concise program to do so by using the generic interface, in which the function names use the prefix P00_, and require the specific problem index to be supplied as an extra input argument:

• P00_AB returns bounds for a problem specified by index.
• P00_F returns the objective function value for a problem specified by index.
• P00_M returns the spatial dimension for a problem specified by index.
• P00_SOL returns known solutions for a problem specified by index.
• P00_TITLE returns a title for a problem specified by index.

### Languages:

test_opt_con is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

### Related Data and Programs:

ASA047, a FORTRAN90 code which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

BRENT, a FORTRAN90 code 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 code which minimizes a scalar function of several variables using the compass search algorithm.

DQED, a FORTRAN90 code which solves constrained least squares problems.

PRAXIS, a FORTRAN90 code which implements the principal axis method of Richard Brent for minimization of a function without the use of derivatives.

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

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

### Reference:

1. Harald Niederreiter, Kevin McCurley,
Optimization of functions by quasi-random search methods,
Computing,
Volume 22, Number 2, 1979, pages 119-123.

### Source Code:

Last revised on 04 September 2020.