Problem 14 and 15

src/ADNLPProblems/boundary.jl

@@ -0,0 +1,46 @@
+export boundary
+
+function boundary(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return boundary(Val(model); kwargs...)
+end
+
+function boundary(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  h = 1 // (n + 1)
+  function f(x; n = length(x))
+    s = zero(T)
+    for i = 1:n
+      xm = (i == 1) ? zero(T) : x[i - 1]
+      xp = (i == n) ? zero(T) : x[i + 1]
+      s += (2 * x[i] - xm - xp + (h^2 / 2) * (x[i] + i * h + 1)^3)^2
+    end
+    return s
+  end
+
+  x0 = Vector{T}(undef, n)
+  for i = 1:n
+    x0[i] = i * h * (1 - i * h)
+  end
+
+  return ADNLPModels.ADNLPModel(f, x0, name = "boundary", minimize = true; kwargs...)
+end
+
+function boundary(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  h = 1 // (n + 1)
+
+  function F!(r, x; n = length(x))
+    @inbounds for i = 1:n
+      xm = (i == 1) ? zero(T) : x[i - 1]
+      xp = (i == n) ? zero(T) : x[i + 1]
+      r[i] = 2 * x[i] - xm - xp + (h^2 / 2) * (x[i] + i * h + 1)^3
+    end
+    return r
+  end
+
+  x0 = Vector{T}(undef, n)
+  for i = 1:n
+    x0[i] = i * h * (1 - i * h)
+  end
+
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "boundary-nls"; kwargs...)
+end

src/ADNLPProblems/variational.jl

@@ -0,0 +1,26 @@
+export variational
+
+function variational(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  h = 1 // (n + 1)
+  x0 = [begin
+    ih = i * h
+    convert(T, ih * (1 - ih))
+    end for i = 1:n]
+  f =
+    x -> begin
+      xext = vcat(zero(eltype(x)), x, zero(eltype(x)))
+      term1 = sum(x[i] * (x[i] - xext[i + 2]) / convert(eltype(x), h) for i = 1:n)
+      term2 = sum(
+        if eltype(x) <: AbstractFloat
+          d = xext[j + 2] - xext[j + 1]
+          abs(d) <= eps(eltype(x)) ? exp(xext[j + 1]) : (exp(xext[j + 2]) - exp(xext[j + 1])) / d
+        else
+          d = xext[j + 2] - xext[j + 1]
+          exp(xext[j + 1]) * expm1(d) / d
+        end for j = 0:n
+      )
+      return 2 * (term1 + n * (convert(eltype(x), h) / 2) * term2)
+    end
+
+  return ADNLPModels.ADNLPModel(f, x0, name = "variational", minimize = true; kwargs...)
+end

src/Meta/boundary.jl

@@ -0,0 +1,27 @@
+boundary_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "boundary",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :least_squares,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => Inf,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :academic,
+)
+
+get_boundary_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_boundary_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nls_nequ(; n::Integer = default_nvar, kwargs...) = n

src/Meta/variational.jl

@@ -0,0 +1,27 @@
+variational_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "variational",
+  :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 => Inf,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :academic,
+)
+
+get_variational_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_variational_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nls_nequ(; n::Integer = default_nvar, kwargs...) = 0

src/PureJuMP/boundary.jl

@@ -0,0 +1,29 @@
+# Discrete boundary value problem
+#
+#   Problem 14 in
+#   L. Luksan, C. Matonoha and J. Vlcek
+#   Sparse Test Problems for Unconstrained Optimization,
+#   Technical Report 1064,
+#   Institute of Computer Science,
+#   Academy of Science of the Czech Republic
+#
+#   https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
+export boundary
+
+function boundary(; n::Int = default_nvar, kwargs...)
+  h = 1 // (n + 1)
+  model = Model()
+  x0 = [i * h * (1 - i * h) for i = 1:n]
+  @variable(model, x[i = 1:n], start = x0[i])
+  @objective(
+    model,
+    Min,
+    sum(
+      (
+        2 * x[i] - (i == 1 ? 0 : x[i - 1]) - (i == n ? 0 : x[i + 1]) +
+        (h^2 / 2) * (x[i] + Float64(i) * h + 1)^3
+      )^2 for i = 1:n
+    )
+  )
+  return model
+end

src/PureJuMP/variational.jl

@@ -0,0 +1,46 @@
+# Discretization of a variational problem
+#
+#   Problem 15 in
+#   L. Luksan, C. Matonoha and J. Vlcek
+#   Sparse Test Problems for Unconstrained Optimization,
+#   Technical Report 1064,
+#   Institute of Computer Science,
+#   Academy of Science of the Czech Republic
+#
+#   https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
+export variational
+
+function variational(; n::Int = default_nvar, kwargs...)
+  h = 1 // (n + 1)
+    x0 = [begin
+        ih = i * h
+        convert(Float64, ih * (1 - ih))
+      end for i = 1:n]
+  model = Model()
+  @variable(model, x[i = 1:n], start = x0[i])
+
+  @objective(
+    model,
+    Min,
+    2 * (
+      (sum(x[i] * (x[i] - x[i + 1]) / h for i = 1:(n - 1)) + x[n] * x[n] / h) +
+      n *
+      (h / 2) *
+      (
+        (1 + x[1]/2 + x[1]^2/6 + x[1]^3/24 + x[1]^4/120) +
+        sum(
+          exp(x[j]) * (
+            1 +
+            (x[j + 1] - x[j]) / 2 +
+            (x[j + 1] - x[j])^2 / 6 +
+            (x[j + 1] - x[j])^3 / 24 +
+            (x[j + 1] - x[j])^4 / 120
+          ) for j = 1:(n - 1)
+        ) +
+        exp(x[n]) * (1 + (0 - x[n]) / 2 + (0 - x[n])^2 / 6 + (0 - x[n])^3 / 24 + (0 - x[n])^4 / 120)
+      )
+    )
+  )
+
+  return model
+end