Available test functions are:
Hald, Nesterov, Nesterov1, Rastrigin, Rosenbrock, Shor. Rosenbrock -- Rosenbrock's famous valley function from 1960. It can
also be regarded as a least-squares problem:
$$\sum_{i=1}^{n-1} (1-x_i)^2 + 100 (x_{i+1}-x_i^2)^2$$
ll{
No. of Vars.: n >= 2
Bounds: -5.12 <= xi="" <="5.12" local="" minima:="" at="" f(-1,="" 1,="" ...,="" 1)="" for="" n="">= 4
Minimum: 0.0
Solution: xi = 1, i = 1:n
}
Nesterov -- Nesterov's smooth adaptation of Rosenbrock, based on the
idea of Chebyshev polynomials. This function is even more difficult to
optimize than Rosenbrock's:
$$(x_1 - 1)^2 / 4 + \sum_{i=1}^{n-1} (1 + x_{i+1} - 2 x_i^2)$$
ll{
No. of Vars.: n >= 2
Bounds: -5.12 <= xi="" <="5.12" local="" minima:="" ?="" minimum:="" 0.0="" solution:="" i="1:n" }<="" p="">
Rastrigin -- Rastrigin's function is a famous, non-convex example from 1989 for global optimization. It is a typical example of a multimodal function with many local minima:
$$10 n + \sum_1^n (x_i^2 - 10 \cos(2 \pi x_i))$$
ll{
No. of Vars.: n >= 2
Bounds: -5.12 <= xi="" <="5.12" local="" minima:="" many="" minimum:="" 0.0="" solution:="" i="1:n" }<="" p="">
Hald -- Hald's function is a typical example of a non-smooth test
function, from Hald and Madsen in 1981.
$$\max_{1 \le i \le n} \frac{x_1 + x_2 t_i}{1 + x_3 t_i + x_4 t_i^2 + x_5 t_i^3} - \exp(t_i)$$
where $t_i = -1 + (i - 1)/10$ for $1 \le i \le 21$.
ll{
No. of Vars.: n =5
Bounds: -1 <= xi="" <="1" local="" minima:="" ?="" minimum:="" 0.0001223713="" solution:="" (0.99987763,="" 0.25358844,="" -0.74660757,="" 0.24520150,="" -0.03749029)="" }<="" p="">
Shor -- Shor's function is another typical example of a non-smooth test
function, a benchmark for Shor's R-algorithm.