Add integreq (#261)

src/ADNLPProblems/integreq.jl

@@ -0,0 +1,38 @@
+export integreq
+
+function integreq(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return integreq(Val(model); kwargs...)
+end
+
+function integreq(
+  ::Val{:nlp};
+  n::Int = default_nvar,
+  type::Val{T} = Val(Float64),
+  kwargs...,
+) where {T}
+  function f(x; n = length(x))
+    h = 1 // (n + 1)
+    return 1 // 2 * sum((x[i] + h * ((1 - i * h) * sum(j * h * (x[j] + j * h + 1)^3 for j=1:i) + i * h * sum((1 - j * h) * (x[j] + j * h + 1)^3 for j=(i + 1):n)) / 2)^2 for i = 1:(n-1)) + 1 // 2 * (x[n] + h * ((1 - n * h) * sum(j * h * (x[j] + j * h + 1)^3 for j=1:n)) / 2)^2
+  end
+  x0 = T[j * (1 / (n + 1)) * (j * (1 / (n + 1)) - 1) for j=1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "integreq"; kwargs...)
+end
+
+function integreq(
+  ::Val{:nls};
+  n::Int = default_nvar,
+  type::Val{T} = Val(Float64),
+  kwargs...,
+) where {T}
+  function F!(r, x; n = length(x))
+    h = 1 // (n + 1)
+    for i = 1:(n - 1)
+      r[i] = x[i] + h * ((1 - i * h) * sum(j * h * (x[j] + j * h + 1)^3 for j=1:i) + i * h * sum((1 - j * h) * (x[j] + j * h + 1)^3 for j=(i + 1):n)) / 2
+    end
+    r[n] = x[n] + h * ((1 - n * h) * sum(j * h * (x[j] + j * h + 1)^3 for j=1:n)) / 2
+    return r
+  end
+  x0 = T[j * (1 / (n + 1)) * (j * (1 / (n + 1)) - 1) for j=1:n]
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "integreq-nls"; kwargs...)
+end

src/Meta/integreq.jl

@@ -0,0 +1,26 @@
+integreq_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "integreq",
+  :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 => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_integreq_nvar(; n::Integer = default_nvar, kwargs...) = 1 * n + 0
+get_integreq_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_integreq_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_integreq_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_integreq_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_integreq_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_integreq_nls_nequ(; n::Integer = default_nvar, kwargs...) = n

src/PureJuMP/integreq.jl

@@ -0,0 +1,34 @@
+#   The discrete integral problem.
+#
+#   Source: problem 29 in
+#      J.J. More, B.S. Garbow and K.E. Hillstrom,
+#      "Testing Unconstrained Optimization Software",
+#      ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
+#   Also problem 165 (p. 74) in
+#      A.R. Buckley,
+#      "Test functions for unconstrained minimization",
+#      TR 1989CS-3, Mathematics, statistics and computing centre,
+#      Dalhousie University, Halifax (CDN), 1989.
+#
+#   classification NOR2-AN-V-V
+
+export integreq
+
+"Linear function with `n` parameters and `m` observations  - full rank"
+function integreq(args...; n::Int = default_nvar, kwargs...)
+  h = 1 / (n + 1)
+
+  nlp = Model()
+
+  @variable(nlp, x[j = 1:n], start = 1.0)
+  x0 = [j * h * (j * h - 1) for j=1:n]
+  set_start_value.(x, x0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    1 / 2 * sum((x[i] + h * ((1 - i * h) * sum(j * h * (x[j] + j * h + 1)^3 for j=1:i) + i * h * sum((1 - j * h) * (x[j] + j * h + 1)^3 for j=(i + 1):n)) / 2)^2 for i = 1:(n-1)) + 1 / 2 * (x[n] + h * ((1 - n * h) * sum(j * h * (x[j] + j * h + 1)^3 for j=1:n)) / 2)^2
+  )
+
+  return nlp
+end