add box2 problem from cutest (#142)

* add box2 problem from cutest

src/ADNLPProblems/BOX2.jl

@@ -0,0 +1,13 @@
+export BOX2
+
+function BOX2(args...; n::Int = default_nvar, type::Val{T} = Val(Float64), m::Int = 10, kwargs...) where {T}
+  m < 3 && @warn("BOX2: must have m ≥ 3")
+  m = max(m, 3)
+
+  x0 = T[0; 10; 1]
+  f(x) = one(T)/2*sum((exp(-one(T)/10*j*x[1]) - exp(-one(T)/10*j*x[2]) -x[3]*(exp(-one(T)/10*j) - exp(-T(j))))^2 for j = 1:m)
+  c(x) = [x[3]]
+  l = ones(T, 1)
+
+  return ADNLPModels.ADNLPModel(f, x0, c, l, l, name = "BOX2", lin = [1]; kwargs...)
+end

src/Meta/BOX2.jl

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+BOX2_meta = Dict(
+  :nvar => 3,
+  :variable_nvar => false,
+  :ncon => 1,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "BOX2",
+  :has_equalities_only => true,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :general,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 0.9422842504428566,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_BOX2_nvar(; n::Integer = default_nvar, kwargs...) = 3
+get_BOX2_ncon(; n::Integer = default_nvar, kwargs...) = 1
+get_BOX2_nlin(; n::Integer = default_nvar, kwargs...) = 1
+get_BOX2_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_BOX2_nequ(; n::Integer = default_nvar, kwargs...) = 1
+get_BOX2_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/PureJuMP/BOX2.jl

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+#   Box problem in 2 variables, obtained by fixing X3 = 1 in BOX2.
+
+#   Source: Problem 11 in
+#   A.R. Buckley,
+#   "Test functions for unconstrained minimization",
+#   TR 1989CS-3, Mathematics, statistics and computing centre,
+#   Dalhousie University, Halifax (CDN), 1989.
+
+#   classification SXR2-AN-3-0
+export BOX2
+
+function BOX2(args...; n::Int = default_nvar, m::Int = 10, kwargs...)
+  m < 3 && @warn("BOX2: must have m ≥ 3")
+  m = max(m, 3)
+
+  nlp = Model()
+
+  x0 = [0.0; 10.0; 1.0]
+  @variable(nlp, x[i=1:3], start = x0[i])
+
+  @NLobjective(
+  nlp,
+  Min,
+  0.5*sum((exp(-0.1*j*x[1]) - exp(-0.1*j*x[2]) -x[3]*(exp(-0.1*j) - exp(-j)))^2 for j = 1:m))
+  @constraint(nlp, x[3] == 1)
+
+  return nlp
+end