Add chebyquad

src/ADNLPProblems/chebyquad.jl

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+export chebyquad
+
+function chebyquad(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return chebyquad(Val(model); kwargs...)
+end
+
+function _cheby_recurrence(xj, i::Integer)
+  i == 0 && return one(xj)
+  i == 1 && return xj
+  tk_prev = one(xj)
+  tk = xj
+  for _ = 2:i
+    tk_next = 2 * xj * tk - tk_prev
+    tk_prev = tk
+    tk = tk_next
+  end
+  return tk
+end
+
+function chebyquad(::Val{:nlp}; n::Int = default_nvar, m::Int = n, type::Type{T} = Float64, kwargs...) where {T}
+  m = max(m, n)
+  function f(x; n = length(x))
+    inv_n = one(eltype(x)) / n
+    s = zero(eltype(x))
+    for i = 1:div(m + 1, 2)
+      acc = zero(eltype(x))
+      for j = 1:n
+        acc += _cheby_recurrence(x[j], 2i - 1)
+      end
+      ri = inv_n * acc
+      s += ri * ri
+    end
+    for i = 1:div(m, 2)
+      acc = zero(eltype(x))
+      for j = 1:n
+        acc += _cheby_recurrence(x[j], 2i)
+      end
+      ri = inv_n * acc + one(eltype(x)) / ((2i)^2 - 1)
+      s += ri * ri
+    end
+    return s / 2
+  end
+  x0 = [j * one(T) / (n + one(T)) for j = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "chebyquad"; kwargs...)
+end
+
+function chebyquad(::Val{:nls}; n::Int = default_nvar, m::Int = n, type::Type{T} = Float64, kwargs...) where {T}
+  m = max(m, n)
+  function F!(r, x)
+    n = length(x)
+    m = length(r)
+    inv_n = one(eltype(x)) / n
+    for i = 1:div(m, 2)
+      acc_odd = zero(eltype(x))
+      acc_even = zero(eltype(x))
+      for j = 1:n
+        acc_odd += _cheby_recurrence(x[j], 2i - 1)
+        acc_even += _cheby_recurrence(x[j], 2i)
+      end
+      r[2i - 1] = inv_n * acc_odd
+      r[2i] = inv_n * acc_even + one(eltype(x)) / ((2i)^2 - 1)
+    end
+    if isodd(m)
+      acc = zero(eltype(x))
+      for j = 1:n
+        acc += _cheby_recurrence(x[j], m)
+      end
+      r[m] = inv_n * acc
+    end
+    return r
+  end
+  x0 = [j * one(T) / (n + one(T)) for j = 1:n]
+  return ADNLPModels.ADNLSModel!(F!, x0, m, name = "chebyquad-nls"; kwargs...)
+end

src/Meta/chebyquad.jl

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+chebyquad_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "chebyquad",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :least_squares,
+  :contype => :unconstrained,
+  :best_known_lower_bound => 0.0,
+  :best_known_upper_bound => Inf,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+  :implementation => :both,
+  :url => "https://bitbucket.org/optrove/sif/src/master/CHEBYQAD.SIF",
+  :notes => raw"""
+The Chebyquad problem in variable dimension. This is a nonlinear least-squares
+problem with n groups. The Hessian is full.
+
+classification SBR2-AN-V-0
+""",
+  :origin_notes => raw"""
+Problem 35 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#133 (p. 44).
+
+SIF input: Nick Gould, March 1990.
+""",
+  :reference => raw"""
+@article{MoreGarbowHillstrom1981,
+  author  = {Mor{\'e}, Jorge J. and Garbow, Burton S. and Hillstrom, Kenneth E.},
+  title   = {Testing Unconstrained Optimization Software},
+  journal = {ACM Transactions on Mathematical Software},
+  year    = {1981},
+  volume  = {7},
+  number  = {1},
+  pages   = {17--41},
+  doi     = {10.1145/355934.355936}
+}
+""",
+  :lib => "CUTEst:CHEBYQAD",
+)
+get_chebyquad_nvar(; n::Int = default_nvar, kwargs...) = n
+get_chebyquad_ncon(; n::Int = default_nvar, kwargs...) = 0
+get_chebyquad_nlin(; n::Int = default_nvar, kwargs...) = 0
+get_chebyquad_nnln(; n::Int = default_nvar, kwargs...) = 0
+get_chebyquad_nequ(; n::Int = default_nvar, kwargs...) = 0
+get_chebyquad_nineq(; n::Int = default_nvar, kwargs...) = 0
+get_chebyquad_nls_nequ(; n::Int = default_nvar, m::Int = n, kwargs...) = max(m, n)

src/PureJuMP/chebyquad.jl

@@ -0,0 +1,33 @@
+export chebyquad
+
+function _cheby_recurrence(xj, i::Integer)
+  i == 0 && return one(xj)
+  i == 1 && return xj
+  tk_prev = one(xj)
+  tk = xj
+  for _ = 2:i
+    tk_next = 2 * xj * tk - tk_prev
+    tk_prev = tk
+    tk = tk_next
+  end
+  return tk
+end
+
+"The Chebyshev quadrature problem in variable dimension"
+function chebyquad(args...; n::Int = default_nvar, m::Int = n, kwargs...)
+  m = max(m, n)
+  nlp = Model()
+  @variable(nlp, x[j = 1:n], start = j / (n + 1))
+  @objective(
+    nlp,
+    Min,
+    0.5 * sum(
+      ((1 / n) * sum(_cheby_recurrence(x[j], 2i - 1) for j = 1:n))^2 for
+      i = 1:div(m + 1, 2)
+    ) + 0.5 * sum(
+      ((1 / n) * sum(_cheby_recurrence(x[j], 2i) for j = 1:n) + 1 / ((2i)^2 - 1))^2 for
+      i = 1:div(m, 2)
+    ),
+  )
+  return nlp
+end