Add AMPGO multivariate test functions (Ackley, Rastrigin, Griewank, Sphere)

Implements four commonly-used multivariate optimization benchmark functions
from the AMPGO test set as part of addressing issue #236. These functions
are widely used in global optimization and provide good test cases for
optimization algorithms.

- Ackley: n-dimensional multimodal function with bounds [-32, 32]
- Rastrigin: n-dimensional highly multimodal function with bounds [-5.12, 5.12]
- Griewank: n-dimensional multimodal function with bounds [-600, 600]
- Sphere: simple n-dimensional convex function with bounds [-1, 1]

All functions follow the standard ADNLPProblems pattern and support
arbitrary dimensions and data types.

Closes #236 (partial - adds 4 of 184 multivariate problems)

Author: arnavk23

src/ADNLPProblems/ackley.jl

@@ -0,0 +1,12 @@
+export ackley
+
+function ackley(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x)
+    n = length(x)
+    sum1 = sum(x[i]^2 for i = 1:n)
+    sum2 = sum(cos(2 * T(π) * x[i]) for i = 1:n)
+    return -20 * exp(-T(0.2) * sqrt(sum1 / n)) - exp(sum2 / n) + 20 + T(ℯ)
+  end
+  x0 = T[-32 + 64 * rand(T) for _ = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "ackley"; kwargs...)
+end

src/ADNLPProblems/griewank.jl

@@ -0,0 +1,12 @@
+export griewank
+
+function griewank(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x)
+    n = length(x)
+    sum_term = sum(x[i]^2 for i = 1:n) / 4000
+    prod_term = prod(cos(x[i] / sqrt(T(i))) for i = 1:n)
+    return sum_term - prod_term + 1
+  end
+  x0 = T[-600 + 1200 * rand(T) for _ = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "griewank"; kwargs...)
+end

src/ADNLPProblems/rastrigin.jl

@@ -0,0 +1,10 @@
+export rastrigin
+
+function rastrigin(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x)
+    n = length(x)
+    return 10 * n + sum(x[i]^2 - 10 * cos(2 * T(π) * x[i]) for i = 1:n)
+  end
+  x0 = T[-5.12 + 10.24 * rand(T) for _ = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "rastrigin"; kwargs...)
+end

src/ADNLPProblems/sphere.jl

@@ -0,0 +1,9 @@
+export sphere
+
+function sphere(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x)
+    return sum(x[i]^2 for i = 1:length(x))
+  end
+  x0 = T[-1 + 2 * rand(T) for _ = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "sphere"; kwargs...)
+end