Problem 9,10 and 16

src/ADNLPProblems/toint.jl

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+export toint
+
+function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+	function f(x; n = length(x))
+		s = zero(T)
+		for i ∈ 1:n
+			ci = 1 + (i // 10)
+			js = max(1, i-2):min(n, i+2)
+				if iseven(n)
+					js = sort(collect(union(collect(js), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n])))
+				end
+
+			for j ∈ js
+				aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+				bij = (i + j) // 10
+				cj = (1 + j) // 10
+				s += aij * sin(bij + ci * x[i] + cj * x[j])
+			end
+		end
+		return s / n
+	end
+
+	x0 = fill(one(T), n)
+	return ADNLPModels.ADNLPModel(f, x0, name = "toint"; kwargs...)
+end

src/ADNLPProblems/trig.jl

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+export trig
+
+function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x; n = length(x))
+    s = zero(T)
+    for i = 1:n
+      s += i * (1 - cos(x[i]))
+
+      js = max(1, i - 2):min(n, i + 2)
+      if iseven(n)
+        js = sort(collect(union(collect(js), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n])))
+      end
+      for j in js
+        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+        bij = (i + j) // 10
+        s += aij * sin(x[j]) + bij * cos(x[j])
+      end
+    end
+    return s / n
+  end
+
+  x0 = fill(one(T) / n, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "trig"; kwargs...)
+end

src/ADNLPProblems/trigb.jl

@@ -0,0 +1,16 @@
+export trigb
+
+function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x; n = length(x))
+    s = zero(T)
+    for i = 1:n
+      xim = (i == 1) ? zero(T) : x[i - 1]
+      xip = (i == n) ? zero(T) : x[i + 1]
+      s += i * (1 - cos(x[i]) + sin(xim) - sin(xip))
+    end
+    return s
+  end
+
+  x0 = fill(one(T), n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
+end

src/Meta/toint.jl

@@ -0,0 +1,26 @@
+toint_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "toint",
+  :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_toint_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_toint_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/Meta/trig.jl

@@ -0,0 +1,26 @@
+trig_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "trig",
+  :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_trig_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_trig_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/Meta/trigb.jl

@@ -0,0 +1,26 @@
+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

src/PureJuMP/toint.jl

@@ -0,0 +1,39 @@
+# Toint trigonometric function
+#
+#   Problem 10 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 toint
+
+function toint(args...; n::Int = default_nvar, kwargs...)
+  model = Model()
+  @variable(model, x[i = 1:n], start = 1)
+
+  @objective(
+    model,
+    Min,
+    (1 / n) * sum(begin
+      ci = 1 + i / 10
+      s = zero(Float64)
+      js = max(1, i - 2):min(n, i + 2)
+      if iseven(n)
+        js = sort(collect(union(collect(js), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n])))
+      end
+      for j in js
+        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+        bij = (i + j) / 10
+        cj = 1 + j / 10
+        s += aij * sin(bij + ci * x[i] + cj * x[j])
+      end
+      s
+    end for i = 1:n)
+  )
+
+  return model
+end

src/PureJuMP/trig.jl

@@ -0,0 +1,32 @@
+# Another trigonometric function
+#
+#   Problem 9 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 trig
+
+function trig(args...; n::Int = default_nvar, kwargs...)
+  model = Model()
+  @variable(model, x[i = 1:n], start = 1 / n)
+
+  @objective(
+    model,
+    Min,
+    (1 / n) * sum(
+      i * (1 - cos(x[i])) +
+      (
+        sum(5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j]) for j in (
+          iseven(n) ? sort(collect(union(collect(max(1, i - 2):min(n, i + 2)), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n]))) : max(1, i - 2):min(n, i + 2)
+        ))
+      ) for i = 1:n
+    )
+  )
+
+  return model
+end

src/PureJuMP/trigb.jl

@@ -0,0 +1,29 @@
+## 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)
+
+  @objective(
+    model,
+    Min,
+    sum(
+      i *
+      ((1 - cos(x[i])) + ((i == 1) ? sin(0) : sin(x[i - 1])) - ((i == n) ? sin(0) : sin(x[i + 1])))
+      for i = 1:n
+    )
+  )
+
+  return model
+end