Add Meta and PureJuMP implementations for AMPGO multivariate functions

Adds Meta metadata and PureJuMP model definitions for the four AMPGO
multivariate test functions (Ackley, Rastrigin, Griewank, Sphere).

Meta files include:
- Problem metadata (dimensions, constraints, bounds)
- Helper functions for getting problem dimensions

PureJuMP files include:
- JuMP model definitions using @variable and @objective
- Support for arbitrary dimensions via n parameter
- Random initial points within specified bounds
- Problem documentation with references

These complement the ADNLPProblems implementations added in the previous commit.

Author: arnavk23

src/Meta/ackley.jl

@@ -0,0 +1,25 @@
+ackley_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "ackley",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 20.0 + exp(1.0),
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_ackley_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_ackley_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_ackley_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_ackley_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_ackley_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_ackley_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/Meta/griewank.jl

@@ -0,0 +1,25 @@
+griewank_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "griewank",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 360001.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_griewank_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_griewank_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_griewank_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_griewank_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_griewank_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_griewank_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/Meta/rastrigin.jl

@@ -0,0 +1,25 @@
+rastrigin_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "rastrigin",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 10000.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_rastrigin_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_rastrigin_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_rastrigin_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_rastrigin_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_rastrigin_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_rastrigin_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/Meta/sphere.jl

@@ -0,0 +1,25 @@
+sphere_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "sphere",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 100.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_sphere_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_sphere_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_sphere_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_sphere_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_sphere_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_sphere_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/PureJuMP/ackley.jl

@@ -0,0 +1,37 @@
+# Ackley test function
+#
+# A multivariate multimodal optimization problem from the
+# AMPGO test set.
+#
+# Problem Ackley in
+# http://infinity77.net/global_optimization/test_functions_nd_A.html
+# Andrea Gavana
+#
+# f(x) = -20*exp(-0.2*sqrt(sum(x_i^2)/n)) - exp(sum(cos(2*pi*x_i))/n) + 20 + e
+#
+# Global minimum: f(0,...,0) = 0
+# Bounds: x_i in [-32, 32] for all i
+
+export ackley
+
+"Ackley multimodal minimization problem"
+function ackley(args...; n::Int = default_nvar, kwargs...)
+  n < 1 && @warn("ackley: number of variables must be ≥ 1")
+  n = max(1, n)
+
+  nlp = Model()
+
+  x0 = [-32 + 64 * rand() for i = 1:n]
+  @variable(nlp, x[i = 1:n], start = x0[i])
+
+  @objective(
+    nlp,
+    Min,
+    -20 * exp(-0.2 * sqrt(sum(x[i]^2 for i = 1:n) / n)) -
+    exp(sum(cos(2 * π * x[i]) for i = 1:n) / n) +
+    20 +
+    exp(1)
+  )
+
+  return nlp
+end

src/PureJuMP/griewank.jl

@@ -0,0 +1,34 @@
+# Griewank test function
+#
+# A multivariate multimodal optimization problem from the
+# AMPGO test set.
+#
+# Problem Griewank in
+# http://infinity77.net/global_optimization/test_functions_nd_G.html
+# Andrea Gavana
+#
+# f(x) = sum(x_i^2)/4000 - prod(cos(x_i/sqrt(i))) + 1
+#
+# Global minimum: f(0,...,0) = 0
+# Bounds: x_i in [-600, 600] for all i
+
+export griewank
+
+"Griewank multimodal minimization problem"
+function griewank(args...; n::Int = default_nvar, kwargs...)
+  n < 1 && @warn("griewank: number of variables must be ≥ 1")
+  n = max(1, n)
+
+  nlp = Model()
+
+  x0 = [-600 + 1200 * rand() for i = 1:n]
+  @variable(nlp, x[i = 1:n], start = x0[i])
+
+  @objective(
+    nlp,
+    Min,
+    sum(x[i]^2 for i = 1:n) / 4000 - prod(cos(x[i] / sqrt(i)) for i = 1:n) + 1
+  )
+
+  return nlp
+end

src/PureJuMP/rastrigin.jl

@@ -0,0 +1,30 @@
+# Rastrigin test function
+#
+# A multivariate highly multimodal optimization problem from the
+# AMPGO test set.
+#
+# Problem Rastrigin in
+# http://infinity77.net/global_optimization/test_functions_nd_R.html
+# Andrea Gavana
+#
+# f(x) = 10*n + sum(x_i^2 - 10*cos(2*pi*x_i))
+#
+# Global minimum: f(0,...,0) = 0
+# Bounds: x_i in [-5.12, 5.12] for all i
+
+export rastrigin
+
+"Rastrigin multimodal minimization problem"
+function rastrigin(args...; n::Int = default_nvar, kwargs...)
+  n < 1 && @warn("rastrigin: number of variables must be ≥ 1")
+  n = max(1, n)
+
+  nlp = Model()
+
+  x0 = [-5.12 + 10.24 * rand() for i = 1:n]
+  @variable(nlp, x[i = 1:n], start = x0[i])
+
+  @objective(nlp, Min, 10 * n + sum(x[i]^2 - 10 * cos(2 * π * x[i]) for i = 1:n))
+
+  return nlp
+end

src/PureJuMP/sphere.jl

@@ -0,0 +1,30 @@
+# Sphere test function
+#
+# A simple multivariate convex optimization problem from the
+# AMPGO test set.
+#
+# Problem Sphere in
+# http://infinity77.net/global_optimization/test_functions_nd_S.html
+# Andrea Gavana
+#
+# f(x) = sum(x_i^2)
+#
+# Global minimum: f(0,...,0) = 0
+# Bounds: x_i in [-1, 1] for all i
+
+export sphere
+
+"Sphere convex minimization problem"
+function sphere(args...; n::Int = default_nvar, kwargs...)
+  n < 1 && @warn("sphere: number of variables must be ≥ 1")
+  n = max(1, n)
+
+  nlp = Model()
+
+  x0 = [-1 + 2 * rand() for i = 1:n]
+  @variable(nlp, x[i = 1:n], start = x0[i])
+
+  @objective(nlp, Min, sum(x[i]^2 for i = 1:n))
+
+  return nlp
+end