trigb.jl

Author: arnavk23

src/ADNLPProblems/trigb.jl

@@ -1,24 +1,19 @@
 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
+    for i = 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) )
+      term = i * (1 - 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)
+  x0 = fill(1, n)
   return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
 end

src/PureJuMP/trigb.jl

@@ -1,18 +1,26 @@
-## 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
-
+## Banded trigonometric problem
+#
+#   Problem 16 in
+#   L. Luksan, C. Matonoha and J. Vlcek
+#   Sparse Test Problems for Unconstrained Optimization,
+#   Technical Report 1064,
+#   Institute of Computer Science,
+#   Academy of Science of the Czech Republic
+#
+#   https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
+#
 export trigb
 
 function trigb(args...; n::Int = default_nvar, kwargs...)
   model = Model()
   @variable(model, x[i = 1:n], start = 1.0)
 
-  @objective(model, Min,
+  @objective(
+    model,
+    Min,
     sum(
       i * (
-        (1 - cos(x[i])) +
-        ((i == 1) ? sin(0.0) : sin(x[i - 1])) -
+        (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
     )