Add watson (#258)

* Add `watson`

src/ADNLPProblems/watson.jl

@@ -0,0 +1,33 @@
+export watson
+
+function watson(;use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return watson(Val(model); kwargs...)
+end
+
+function watson(::Val{:nlp}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  n = min(max(n, 2), 31)
+  function f(x; n = n)
+    Ti = eltype(x)
+    return 1 // 2 * sum((
+      sum((j - 1) * x[j] * (Ti(i) / 29)^(j-2) for j=2:n) - sum(x[j] * (Ti(i) / 29)^(j-1) for j=1:n)^2 - 1
+    )^2 for i=1:29) + 1 // 2 * (sum((j - 1) * x[j] * x[1]^(j-2) for j=2:n) - sum(x[j] * x[1]^(j-1) for j=1:n)^2 - 1)^2 + 1 // 2 * (sum((j - 1) * x[j] * (x[2] - x[1]^2 - 1)^(j-2) for j=2:n) - sum(x[j] * (x[2] - x[1]^2 - 1)^(j-1) for j=1:n)^2 - 1)
+  end
+  x0 = zeros(T, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "watson"; kwargs...)
+end
+
+function watson(::Val{:nls}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  n = min(max(n, 2), 31)
+  function F!(r, x; n = n)
+    Ti = eltype(x)
+    for i=1:29
+      r[i] = sum((j - 1) * x[j] * (Ti(i) / 29)^(j-2) for j=2:n) - sum(x[j] * (Ti(i) / 29)^(j-1) for j=1:n)^2 - 1
+    end
+    r[30] = sum((j - 1) * x[j] * x[1]^(j-2) for j=2:n) - sum(x[j] * x[1]^(j-1) for j=1:n)^2 - 1
+    r[31] = sum((j - 1) * x[j] * (x[2] - x[1]^2 - 1)^(j-2) for j=2:n) - sum(x[j] * (x[2] - x[1]^2 - 1)^(j-1) for j=1:n)^2 - 1
+    return r
+  end
+  x0 = zeros(T, n)
+  return ADNLPModels.ADNLSModel!(F!, x0, 31, name = "watson-nls"; kwargs...)
+end

src/Meta/watson.jl

@@ -0,0 +1,26 @@
+watson_meta = Dict(
+  :nvar => 31,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "watson",
+  :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 => 500.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_watson_nvar(; n::Integer = default_nvar, kwargs...) = min(max(n, 2), 31)
+get_watson_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_watson_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_watson_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_watson_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_watson_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_watson_nls_nequ(; n::Integer = default_nvar, kwargs...) = 31

src/PureJuMP/watson.jl

@@ -0,0 +1,36 @@
+#
+#   Watson problem in varaible dimension ( 2 <= n <= 31 ).
+#   This function is a nonlinear least squares with 31 groups. 
+#
+#   Source:  problem 20 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 128 (p. 100) in 
+#      A.R. Buckley,
+#      "Test functions for unconstrained minimization",
+#      TR 1989CS-3, Mathematics, statistics and computing centre,
+#      Dalhousie University, Halifax (CDN), 1989.
+#
+#   SUR2-AN-V-0
+
+export watson
+
+function watson(args...; n::Int = default_nvar, kwargs...)
+  n = min(max(n, 2), 31)
+  m = 31
+
+  nlp = Model()
+
+  @variable(nlp, x[j = 1:n], start = 0.0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    0.5 * sum((
+      sum((j - 1) * x[j] * (i / 29)^(j-2) for j=2:n) - sum(x[j] * (i / 29)^(j-1) for j=1:n)^2 - 1
+    )^2 for i=1:29) + 0.5 * (sum((j - 1) * x[j] * x[1]^(j-2) for j=2:n) - sum(x[j] * x[1]^(j-1) for j=1:n)^2 - 1)^2 + 0.5 * (sum((j - 1) * x[j] * (x[2] - x[1]^2 - 1)^(j-2) for j=2:n) - sum(x[j] * (x[2] - x[1]^2 - 1)^(j-1) for j=1:n)^2 - 1)
+  )
+
+  return nlp
+end