`BenchmarkFunctions.ackley_1`

— Method```
ackley_1(X)
ackley_1(X, n=3)
```

Compute the n-dimensional Ackley function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-32,32].

`BenchmarkFunctions.ackley_2`

— Method`ackley_2(X)`

Compute the 2-dimensional Ackley No. 2 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-32, 32] for `i`

= 1, 2.

`BenchmarkFunctions.ackley_3`

— Method`ackley_3(X)`

Compute the 2-dimensional Ackley No. 3 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-32, 32] for `i`

= 1, 2.

`BenchmarkFunctions.ackley_4`

— Method```
ackley_4(X)
ackley_4(X, n=3)
```

Compute the n-dimensional Ackley No. 4 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-35, 35].

`BenchmarkFunctions.adjiman`

— Method`adjiman(X)`

Compute the 2-dimensional Adjiman function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-1, 1] for `i`

= 1, 2. Has specific constraints.

`BenchmarkFunctions.alpine_1`

— Method```
alpine_1(X)
alpine_1(X, n=3)
```

Compute the n-dimensional Alpine No. 1 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-10, 10].

`BenchmarkFunctions.alpine_2`

— Method```
alpine_2(X)
alpine_2(X, n=3)
```

Compute the n-dimensional Alpine No. 2 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [0, 10].

`BenchmarkFunctions.attributes`

— Method`attributes(; string)`

Display either:

- a general list of attributes
- a list of attributes for a benchmark function
- a list of benchmark functions with that attribute

**Examples**

`BenchmarkFunctions.bartels_conn`

— Method`bartels_conn(X)`

Compute the 2-dimensional Bartels-Conn function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-500, 500] for `i`

= 1, 2.

`BenchmarkFunctions.beale`

— Method`beale(X)`

Compute the 2-dimensional Beale function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-4.5, 4.5] for `i`

= 1, 2.

`BenchmarkFunctions.bird`

— Method`bird(X)`

Compute the 2-dimensional Bird function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-2π, 2π] for `i`

= 1, 2.

`BenchmarkFunctions.bohachevsky_1`

— Method`bohachevsky_1(X)`

Compute the 2-dimensional Bohachevsky No. 1 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-100, 100] for `i`

= 1, 2.

`BenchmarkFunctions.bohachevsky_2`

— Method`bohachevsky_2(X)`

Compute the 2-dimensional Bohachevsky No. 2 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-100, 100] for `i`

= 1, 2.

`BenchmarkFunctions.bohachevsky_3`

— Method`bohachevsky_3(X)`

Compute the 2-dimensional Bohachevsky No. 3 function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-100, 100] for `i`

= 1, 2.

`BenchmarkFunctions.brent`

— Method`brent(X)`

Compute the 2-dimensional Brent function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-10, 10] for i = 1, 2.

`BenchmarkFunctions.deckkers_aarts`

— Method`deckkers_aarts(X)`

Compute the 2-dimensional Deckkers-Aarts function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-20, 20] for i = 1, 2.

`BenchmarkFunctions.gramacy_lee`

— Method`gramacy_lee(X)`

Compute the 1-dimensional Gramacy-Lee function on sample vector `X`

.

The function is usually evaluated on `x`

∈ [-0.5, 2.5].

`BenchmarkFunctions.himmelblau`

— Method`himmelblau(X)`

Compute the 2-dimensional Himmelblau function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-6, 6] for `i`

= 1, 2.

`BenchmarkFunctions.mccormick`

— Method`mccormick(X)`

Compute the 2-dimensional McCormick function on sample vector `X`

.

The function is usually evaluated on `x₁`

∈ [-1.5, 4] and `x₂`

∈ [-3, 3]

`BenchmarkFunctions.ndgrid`

— Method`ndgrid(grids...)`

Create an n-dimensional grid over `grids`

– iterables along each dimension.

**Examples**

```
julia> ndgrid(0:1)
2-element Array{Tuple{Int64},1}:
(0,)
(1,)
```

`jldoctest julia> ndgrid((0:1,0:1)) 4-element Array{Tuple{Int64,Int64},1}: (0, 0) (1, 0) (0, 1) (1, 1)`

`BenchmarkFunctions.rosenbrock`

— Method```
rosenbrock(X)
rosenbrock(X, n=3)
```

Compute the n-dimensional Rosenbrock function on sample vector `X`

.

The function is usually evaluated on `xᵢ`

∈ [-5, 10] or `xᵢ`

∈ [-2.048, -2.048].