feat(trigb): add banded trigonometric problem (Meta, ADNLP, PureJuMP)

Author: arnavk23

src/ADNLPProblems/trigb.jl

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+export trigb
+
+function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  # Band-limited trigonometric objective
+  # F(x) = sum_{i=1}^n i * [ (1 - cos(x_i)) + sin(x_{i-1}) - sin(x_{i+1}) ]
+  # with boundary values x_0 = x_{n+1} = 0
+
+  function f(x; n = length(x))
+    n_local = n
+    s = zero(T)
+    for i in 1:n_local
+      xi = x[i]
+      left = (i == 1) ? zero(T) : x[i - 1]
+      right = (i == n_local) ? zero(T) : x[i + 1]
+      term = T(i) * ( (one(T) - cos(xi)) + sin(left) - sin(right) )
+      s += term
+    end
+    return s
+  end
+
+  # default initial guess: xbar_i = 1 (use type-generic one(T))
+  x0 = fill(one(T), n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
+end

src/Meta/trigb.jl

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+trigb_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "trigb",
+  :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 => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+
+get_trigb_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_trigb_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n

src/PureJuMP/trigb.jl

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+## Banded trigonometric problem (Problem 16)
+## F(x) = sum_{i=1}^n i * [ (1 - cos(x_i)) + sin(x_{i-1}) - sin(x_{i+1}) ]
+## boundary: x_0 = x_{n+1} = 0
+
+export trigb
+
+function trigb(args...; n::Int = default_nvar, kwargs...)
+  model = Model()
+  @variable(model, x[i = 1:n], start = 1.0)
+
+  @objective(model, Min,
+    sum(
+      i * (
+        (1 - cos(x[i])) +
+        ((i == 1) ? sin(0.0) : sin(x[i - 1])) -
+        ((i == n) ? sin(0.0) : sin(x[i + 1]))
+      ) for i = 1:n
+    )
+  )
+
+  return model
+end