Problem 14 and 15 (#385)

* Problem 14 and 15

---------

Co-authored-by: Tangi Migot <tangi.migot@gmail.com>

Author: arnavk23

src/ADNLPProblems/boundary.jl

@@ -0,0 +1,46 @@
+export boundary
+
+function boundary(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return boundary(Val(model); kwargs...)
+end
+
+function boundary(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  h = 1 // (n + 1)
+  function f(x; n = length(x))
+    s = zero(T)
+    @inbounds for i = 1:n
+      xm = (i == 1) ? zero(T) : x[i - 1]
+      xp = (i == n) ? zero(T) : x[i + 1]
+      s += (2 * x[i] - xm - xp + (h^2 / 2) * (x[i] + i * h + 1)^3)^2
+    end
+    return s
+  end
+
+  x0 = Vector{T}(undef, n)
+  for i = 1:n
+    x0[i] = i * h * (1 - i * h)
+  end
+
+  return ADNLPModels.ADNLPModel(f, x0, name = "boundary"; kwargs...)
+end
+
+function boundary(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  h = 1 // (n + 1)
+
+  function F!(r, x; n = length(x))
+    @inbounds for i = 1:n
+      xm = (i == 1) ? zero(T) : x[i - 1]
+      xp = (i == n) ? zero(T) : x[i + 1]
+      r[i] = 2 * x[i] - xm - xp + (h^2 / 2) * (x[i] + i * h + 1)^3
+    end
+    return r
+  end
+
+  x0 = Vector{T}(undef, n)
+  for i = 1:n
+    x0[i] = i * h * (1 - i * h)
+  end
+
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "boundary-nls"; kwargs...)
+end

src/ADNLPProblems/variational.jl

@@ -0,0 +1,31 @@
+export variational
+
+function variational(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  h = 1 // (n + 1)
+  x0 = T[(i * h) * (1 - i * h) for i = 1:n]
+
+function f(x; n = length(x))
+  Ti = eltype(x)
+
+  term1 = zero(Ti)
+  term2 = zero(Ti)
+  @inbounds for k = 1:n
+    xi  = x[k]
+    xip = (k < n) ? x[k + 1] : zero(Ti)
+
+    term1 += xi * (xi - xip) / h
+
+    a_prev = (k == 1) ? zero(Ti) : x[k - 1]
+    b_prev = xi
+    term2 += (exp(b_prev) - exp(a_prev)) / (b_prev - a_prev)
+
+    if k == n
+      a_last, b_last = xi, zero(Ti)
+      term2 += (exp(b_last) - exp(a_last)) / (b_last - a_last)
+    end
+  end
+  return 2 * (term1 + 2 * h * term2)
+end
+
+  return ADNLPModels.ADNLPModel(f, x0, name = "variational"; kwargs...)
+end

src/Meta/boundary.jl

@@ -0,0 +1,27 @@
+boundary_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "boundary",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :least_squares,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => Inf,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :academic,
+)
+
+get_boundary_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_boundary_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_boundary_nls_nequ(; n::Integer = default_nvar, kwargs...) = n

src/Meta/variational.jl

@@ -0,0 +1,27 @@
+variational_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "variational",
+  :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 => Inf,
+  :is_feasible => true,
+  :defined_everywhere => false,
+  :origin => :academic,
+)
+
+get_variational_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_variational_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_variational_nls_nequ(; n::Integer = default_nvar, kwargs...) = 0

src/PureJuMP/boundary.jl

@@ -0,0 +1,29 @@
+# Discrete boundary value problem
+#
+#   Problem 14 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 boundary
+
+function boundary(; n::Int = default_nvar, kwargs...)
+  h = 1 // (n + 1)
+  model = Model()
+  x0 = [i * h * (1 - i * h) for i = 1:n]
+  @variable(model, x[i = 1:n], start = x0[i])
+  @objective(
+    model,
+    Min,
+    sum(
+      (
+        2 * x[i] - (i == 1 ? 0 : x[i - 1]) - (i == n ? 0 : x[i + 1]) +
+        (h^2 / 2) * (x[i] + i * h + 1)^3
+      )^2 for i = 1:n
+    )
+  )
+  return model
+end

src/PureJuMP/variational.jl

@@ -0,0 +1,34 @@
+# Discretization of a variational problem
+#
+#   Problem 15 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 variational
+
+function variational(; n::Int = default_nvar, kwargs...)
+  h = 1 // (n + 1)
+  x0 = [(i * h) * (1 - i * h) for i = 1:n]
+  model = Model()
+  @variable(model, x[i = 1:n], start = x0[i])
+
+  @objective(
+    model,
+    Min,
+    2 * (
+      (sum(x[i] * (x[i] - x[i + 1]) / h for i ∈ 1:(n - 1)) + x[n] * x[n] / h) +
+      2 * h *
+      (
+        (exp(x[1]) - exp(0)) / (x[1] - 0) +
+        sum((exp(x[j + 1]) - exp(x[j])) / (x[j + 1] - x[j]) for j ∈ 1:(n - 1)) +
+        (exp(0) - exp(x[n])) / (0 - x[n])
+      )
+    )
+  )
+
+  return model
+end