AMPGO multivariate implementation

src/ADNLPProblems/ackley.jl

@@ -0,0 +1,14 @@
+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 = zeros(T, n)
+  lvar = fill(T(-32.768), n)
+  uvar = fill(T(32.768), n)
+  return ADNLPModels.ADNLPModel(f, x0; lvar = lvar, uvar = uvar, name = "ackley", kwargs...)
+end

src/ADNLPProblems/griewank.jl

@@ -0,0 +1,19 @@
+export griewank
+
+function griewank(; n::Int = default_nvar, type::Type{T} = Float64, x0::Union{Nothing,AbstractVector} = nothing, kwargs...) where {T}
+  function f(x)
+    n = length(x)
+    sum_term = sum(x[i]^2 for i = 1:n) / T(4000)
+    prod_term = prod(cos(x[i] / sqrt(T(i))) for i = 1:n)
+    return sum_term - prod_term + one(T)
+  end
+  if x0 === nothing
+    x0 = zeros(T, n)
+  else
+    length(x0) == n || throw(ArgumentError("griewank: length(x0) = $(length(x0)) must equal n = $n"))
+    x0 = T.(x0)
+  end
+  lvar = fill(T(-600), n)
+  uvar = fill(T(600), n)
+  return ADNLPModels.ADNLPModel(f, x0; lvar = lvar, uvar = uvar, name = "griewank", kwargs...)
+end

src/ADNLPProblems/rastrigin.jl

@@ -0,0 +1,12 @@
+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 = zeros(T, n)
+  lvar = fill(T(-5.12), n)
+  uvar = fill(T(5.12), n)
+  return ADNLPModels.ADNLPModel(f, x0, lvar = lvar, uvar = uvar, name = "rastrigin"; kwargs...)
+end

src/ADNLPProblems/sphere.jl

@@ -0,0 +1,11 @@
+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 = zeros(T, n)
+  lvar = fill(T(-1), n)
+  uvar = fill(T(1), n)
+  return ADNLPModels.ADNLPModel(f, x0; lvar = lvar, uvar = uvar, name = "sphere", kwargs...)
+end

src/Meta/ackley.jl

@@ -0,0 +1,48 @@
+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 => true,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => 0.0,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :modelling,
+  :implementation => :both,
+  :url => "https://doi.org/10.1007/978-1-4613-1997-9",
+  :notes => raw"""
+A non-convex multimodal function commonly used as a performance test problem for
+global optimization algorithms. The function has a global minimum of 0 at the origin
+and is surrounded by a nearly flat outer region that makes gradient-based methods difficult.
+The search domain is [-32.768, 32.768]^n.
+""",
+  :origin_notes => raw"""
+Proposed by David Ackley in his 1987 PhD dissertation.
+The n-dimensional generalization is due to Bäck and Schwefel (1993).
+""",
+  :reference => raw"""
+@book{Ackley1987,
+  author    = {Ackley, David H.},
+  title     = {A Connectionist Machine for Genetic Hillclimbing},
+  publisher = {Kluwer Academic Publishers},
+  address   = {Boston, MA},
+  year      = {1987},
+  doi       = {10.1007/978-1-4613-1997-9}
+}
+""",
+  :lib => "",
+)
+get_ackley_nvar(; n::Int = default_nvar, kwargs...) = n
+get_ackley_ncon(; n::Int = default_nvar, kwargs...) = 0
+get_ackley_nlin(; n::Int = default_nvar, kwargs...) = 0
+get_ackley_nnln(; n::Int = default_nvar, kwargs...) = 0
+get_ackley_nequ(; n::Int = default_nvar, kwargs...) = 0
+get_ackley_nineq(; n::Int = default_nvar, kwargs...) = 0

src/Meta/griewank.jl

@@ -0,0 +1,49 @@
+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 => true,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => 0.0,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :modelling,
+  :implementation => :both,
+  :url => "https://doi.org/10.1007/BF00933356",
+  :notes => raw"""
+A multimodal function composed of a quadratic term and a cosine modulation.
+The global minimum of 0 is at the origin. The search domain is [-600, 600]^n.
+The function becomes easier as dimension increases due to the product term
+being averaged out.
+""",
+  :origin_notes => raw"""
+Introduced by Andreas Griewank in 1981.
+""",
+  :reference => raw"""
+@article{Griewank1981,
+  author  = {Griewank, Andreas O.},
+  title   = {Generalized Descent for Global Optimization},
+  journal = {Journal of Optimization Theory and Applications},
+  volume  = {34},
+  number  = {1},
+  pages   = {11--39},
+  year    = {1981},
+  doi     = {10.1007/BF00933356}
+}
+""",
+  :lib => "",
+)
+get_griewank_nvar(; n::Int = default_nvar, kwargs...) = n
+get_griewank_ncon(; n::Int = default_nvar, kwargs...) = 0
+get_griewank_nlin(; n::Int = default_nvar, kwargs...) = 0
+get_griewank_nnln(; n::Int = default_nvar, kwargs...) = 0
+get_griewank_nequ(; n::Int = default_nvar, kwargs...) = 0
+get_griewank_nineq(; n::Int = default_nvar, kwargs...) = 0

src/Meta/rastrigin.jl

@@ -0,0 +1,47 @@
+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 => true,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => 0.0,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :modelling,
+  :implementation => :both,
+  :url => "",
+  :notes => raw"""
+A non-convex multimodal function based on cosine modulation. The global minimum
+of 0 is at the origin. The search domain is [-5.12, 5.12]^n. The large number
+of local minima makes it a difficult test problem for global optimizers.
+""",
+  :origin_notes => raw"""
+First proposed by L.A. Rastrigin in 1974 as a 2-dimensional function.
+The n-dimensional generalization is due to Rudolph (1990) and was popularized
+by Hoffmeister & Bäck (1991) and Mühlenbein et al. (1991).
+""",
+  :reference => raw"""
+@book{Rastrigin1974,
+  author    = {Rastrigin, L. A.},
+  title     = {Systems of Extremal Control},
+  publisher = {Nauka},
+  address   = {Moscow},
+  year      = {1974}
+}
+""",
+  :lib => "",
+)
+get_rastrigin_nvar(; n::Int = default_nvar, kwargs...) = n
+get_rastrigin_ncon(; n::Int = default_nvar, kwargs...) = 0
+get_rastrigin_nlin(; n::Int = default_nvar, kwargs...) = 0
+get_rastrigin_nnln(; n::Int = default_nvar, kwargs...) = 0
+get_rastrigin_nequ(; n::Int = default_nvar, kwargs...) = 0
+get_rastrigin_nineq(; n::Int = default_nvar, kwargs...) = 0

src/Meta/sphere.jl

@@ -0,0 +1,48 @@
+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 => true,
+  :has_fixed_variables => false,
+  :objtype => :quadratic,
+  :contype => :unconstrained,
+  :best_known_lower_bound => 0.0,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :modelling,
+  :implementation => :both,
+  :url => "https://doi.org/10.1145/355934.355936",
+  :notes => raw"""
+The simplest convex test function: sum of squares. The global minimum of 0 is
+at the origin. The search domain is [-1, 1]^n in this implementation.
+""",
+  :origin_notes => raw"""
+A classic unconstrained optimization test problem, also known as the De Jong
+function 1. Commonly listed as problem 1 in Moré, Garbow and Hillstrom (1981).
+""",
+  :reference => raw"""
+@article{MoreGarbowHillstrom1981,
+  author  = {Mor{\'e}, Jorge J. and Garbow, Burton S. and Hillstrom, Kenneth E.},
+  title   = {Testing Unconstrained Optimization Software},
+  journal = {ACM Transactions on Mathematical Software},
+  year    = {1981},
+  volume  = {7},
+  number  = {1},
+  pages   = {17--41},
+  doi     = {10.1145/355934.355936}
+}
+""",
+  :lib => "",
+)
+get_sphere_nvar(; n::Int = default_nvar, kwargs...) = n
+get_sphere_ncon(; n::Int = default_nvar, kwargs...) = 0
+get_sphere_nlin(; n::Int = default_nvar, kwargs...) = 0
+get_sphere_nnln(; n::Int = default_nvar, kwargs...) = 0
+get_sphere_nequ(; n::Int = default_nvar, kwargs...) = 0
+get_sphere_nineq(; n::Int = default_nvar, kwargs...) = 0

src/PureJuMP/ackley.jl

@@ -0,0 +1,23 @@
+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 = zeros(n)
+  @variable(nlp, -32.768 <= x[i = 1:n] <= 32.768, 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 +1,24 @@
+export griewank
+
+"Griewank multimodal minimization problem"
+function griewank(args...; n::Int = default_nvar, x0::Union{Nothing,AbstractVector} = nothing, kwargs...)
+  n < 1 && @warn("griewank: number of variables must be ≥ 1")
+  n = max(1, n)
+
+  nlp = Model()
+
+  if x0 === nothing
+    x0 = zeros(n)
+  elseif length(x0) != n
+    throw(ArgumentError("griewank: length(x0) = $(length(x0)) must equal n = $n"))
+  end
+  @variable(nlp, -600 <= x[i = 1:n] <= 600, 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 +1,16 @@
+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 = [0.0 for i = 1:n]
+  @variable(nlp, x[i = 1:n], lower_bound = -5.12, upper_bound = 5.12, 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 +1,16 @@
+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 = zeros(n)
+  @variable(nlp, -1 <= x[i = 1:n] <= 1, start = x0[i])
+
+  @objective(nlp, Min, sum(x[i]^2 for i = 1:n))
+
+  return nlp
+end