Added Gaussian fct (#143)

src/ADNLPProblems/gaussian.jl

@@ -0,0 +1,10 @@
+export gaussian
+
+function gaussian(args...; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  function f(x)
+    y = T[.0009, .0044, .0175, .054, .1295, .242, .3521, .3989, .3521, .242, .1295, .054, .0175, .0044, .0009]
+    return sum( (x[1]*exp(-x[2]/2*(T(8-i)/2-x[3])^2)-y[i])^2 for i=1:15)
+  end
+  x0 = T[.4, 1, 0]
+  return ADNLPModels.ADNLPModel(f, x0, name = "gaussian"; kwargs...)
+end

src/Meta/gaussian.jl

@@ -0,0 +1,25 @@
+gaussian_meta = Dict(
+  :nvar => 3,
+  :variable_nvar => false,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "gaussian",
+  :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 => 3.888106991166885e-6,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_gaussian_nvar(; n::Integer = default_nvar, kwargs...) = 3
+get_gaussian_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_gaussian_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_gaussian_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_gaussian_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_gaussian_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/PureJuMP/gaussian.jl

@@ -0,0 +1,28 @@
+#   Source: Problem 9 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.
+
+#   See also Buckley#28
+
+#   classification SUR2-AN-3-0
+export gaussian
+
+function gaussian(args...; n::Int = default_nvar, kwargs...)
+  nlp = Model()
+
+  x0 = [.4, 1, 0]
+  @variable(nlp, x[i=1:3], start=x0[i])
+
+  y = [.0009, .0044, .0175, .054, .1295, .242, .3521, .3989, .3521, .242, .1295, .054, .0175, .0044, .0009]
+
+  @NLobjective(nlp, Min, (x[1]*exp(-x[2]/2*((8-1)/2-x[3])^2)-y[1])^2 + (x[1]*exp(-x[2]/2*((8-2)/2-x[3])^2)-y[2])^2
+      + (x[1]*exp(-x[2]/2*((8-3)/2-x[3])^2)-y[3])^2 + (x[1]*exp(-x[2]/2*((8-4)/2-x[3])^2)-y[4])^2
+      + (x[1]*exp(-x[2]/2*((8-5)/2-x[3])^2)-y[5])^2+ (x[1]*exp(-x[2]/2*((8-6)/2-x[3])^2)-y[6])^2
+      + (x[1]*exp(-x[2]/2*((8-7)/2-x[3])^2)-y[7])^2+ (x[1]*exp(-x[2]/2*((8-8)/2-x[3])^2)-y[8])^2
+      + (x[1]*exp(-x[2]/2*((8-9)/2-x[3])^2)-y[9])^2+ (x[1]*exp(-x[2]/2*((8-10)/2-x[3])^2)-y[10])^2
+      + (x[1]*exp(-x[2]/2*((8-11)/2-x[3])^2)-y[11])^2+ (x[1]*exp(-x[2]/2*((8-12)/2-x[3])^2)-y[12])^2
+      + (x[1]*exp(-x[2]/2*((8-13)/2-x[3])^2)-y[13])^2+ (x[1]*exp(-x[2]/2*((8-14)/2-x[3])^2)-y[14])^2
+      + (x[1]*exp(-x[2]/2*((8-15)/2-x[3])^2)-y[15])^2  )
+  return nlp
+end