Add problems argtrig, bard, biggs5, brownal and broyden3d

src/ADNLPProblems/argtrig.jl

@@ -0,0 +1,13 @@
+export argtrig
+
+function argtrig(
+  ;n::Int = default_nvar,
+  type::Val{T} = Val(Float64),
+  kwargs...,
+) where {T}
+  function f(x; n = length(x))
+    return n - sum(cos(x[j]) + j * (1 - cos(x[j])) - sin(x[j]) for j=1:n)
+  end
+  x0 = 1 // n * ones(T, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "argtrig"; kwargs...)
+end

src/ADNLPProblems/bard.jl

@@ -0,0 +1,27 @@
+export bard
+
+function bard(;use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return bard(Val(model); kwargs...)
+end
+
+function bard(::Val{:nlp}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  y = Rational{Int}[0.14 0.18 0.22 0.25 0.29 0.32 0.35 0.39 0.37 0.58 0.73 0.16 1.34 2.10 4.39 ];
+  function f(x)
+    return 1 // 2 * sum(y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3])) for i = 1:15)
+  end
+  x0 = ones(T, 3)
+  return ADNLPModels.ADNLPModel(f, x0, name = "bard"; kwargs...)
+end
+
+function bard(::Val{:nls}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+    y = Rational{Int}[0.14 0.18 0.22 0.25 0.29 0.32 0.35 0.39 0.37 0.58 0.73 0.16 1.34 2.10 4.39 ];
+    function F!(r, x, y = y)
+    for i=1:15
+      r[i] = y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3]))
+    end
+    return r
+  end
+  x0 = ones(T, 3)
+  return ADNLPModels.ADNLSModel!(F!, x0, 15, name = "bard-nls"; kwargs...)
+end

src/ADNLPProblems/biggs5.jl

@@ -0,0 +1,22 @@
+export biggs5
+
+function biggs5(;
+  n::Int = default_nvar,
+  type::Val{T} = Val(Float64),
+  m::Int = 13,
+  kwargs...,
+) where {T}
+  m = max(6, m)
+  z = [i // 10 for i = 1:m]
+  y = T[exp(-zi) - 5 * exp(-10 * zi) + 3 * exp(-4 * zi) for zi in z]
+  function f(x; m = m, z = z, y = y)
+    return sum(
+      x[3] * exp(-x[1] * z[i]) - x[4] * exp(-x[2] * z[i]) + x[6] * exp(-x[5] * z[i]) - y[i] for i = 1:m
+    )
+  end
+  x0 = ones(T, 6)
+  x0[2] = 2
+  lvar = vcat(-T(Inf) * ones(T, 5), T(3))
+  uvar = vcat(T(Inf) * ones(T, 5), T(3))
+  return ADNLPModels.ADNLPModel(f, x0, lvar, uvar, name = "biggs5"; kwargs...)
+end

src/ADNLPProblems/brownal.jl

@@ -0,0 +1,29 @@
+export brownal
+
+function brownal(;use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return brownal(Val(model); kwargs...)
+end
+
+function brownal(::Val{:nlp}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  function f(x; n = length(x))
+    sj = sum(x[j] for j = 1:n)
+    pj = prod(x[j] for j = 1:n)
+    return 1 // 2 * sum((x[i] + sj - (n + 1))^2 for i = 1:(n-1)) + 1 // 2 * (pj - 1)^2
+  end
+  x0 = 1 // 2 * ones(T, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "brownal"; kwargs...)
+end
+
+function brownal(::Val{:nls}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  function F!(r, x; n = length(x))
+    sj = sum(x[j] for j = 1:n)
+    for i=1:(n-1)
+      r[i] = x[i] + sj - (n + 1)
+    end
+    r[n] = prod(x[j] for j = 1:n) - 1
+    return r
+  end
+  x0 = 1 // 2 * ones(T, n)
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "brownal-nls"; kwargs...)
+end

src/ADNLPProblems/broyden3d.jl

@@ -0,0 +1,27 @@
+export broyden3d
+
+function broyden3d(;use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return broyden3d(Val(model); kwargs...)
+end
+
+function broyden3d(::Val{:nlp}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  function f(x; n = length(x))
+    return 1 // 2 * sum(((3 - 2 * x[i]) * x[i] - x[i - 1] - 2 * x[i + 1] + 1)^2 for i = 2:(n-1) ) + 1 // 2 *  ( (3 - 2 * x[1]) * x[1] - 2 * x[2] + 1)^2 + 1 // 2 * ((3 - 2 * x[n]) * x[n] - x[n - 1] + 1)^2
+  end
+  x0 = -ones(T, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "broyden3d"; kwargs...)
+end
+
+function broyden3d(::Val{:nls}; n::Int = default_nvar, type::Val{T} = Val(Float64), kwargs...) where {T}
+  function F!(r, x; n = length(x))
+    r[1] = (3 - 2 * x[1]) * x[1] - 2 * x[2] + 1
+    r[n] = (3 - 2 * x[n]) * x[n] - x[n - 1] + 1
+    for i=2:(n-1)
+      r[i] = (3 - 2 * x[i]) * x[i] - x[i - 1] - 2 * x[i + 1] + 1
+    end
+    return r
+  end
+  x0 = -ones(T, n)
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "broyden3d-nls"; kwargs...)
+end

src/Meta/argtrig.jl

@@ -0,0 +1,26 @@
+argtrig_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "argtrig",
+  :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_argtrig_nvar(; n::Integer = default_nvar, kwargs...) = 1 * n + 0
+get_argtrig_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_argtrig_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_argtrig_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_argtrig_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_argtrig_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_argtrig_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n

src/Meta/bard.jl

@@ -0,0 +1,26 @@
+bard_meta = Dict(
+  :nvar => 3,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "bard",
+  :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 => 500.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_bard_nvar(; n::Integer = default_nvar, kwargs...) = 3
+get_bard_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_bard_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_bard_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_bard_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_bard_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_bard_nls_nequ(; n::Integer = default_nvar, kwargs...) = 15

src/Meta/biggs5.jl

@@ -0,0 +1,25 @@
+biggs5_meta = Dict(
+  :nvar => 6,
+  :variable_nvar => false,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "biggs5",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => true,
+  :has_fixed_variables => true,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => -3.156207810643302,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_biggs5_nvar(; n::Integer = default_nvar, kwargs...) = 6
+get_biggs5_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_biggs5_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_biggs5_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_biggs5_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_biggs5_nineq(; n::Integer = default_nvar, kwargs...) = 0

src/Meta/brownal.jl

@@ -0,0 +1,26 @@
+brownal_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "brownal",
+  :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 => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_brownal_nvar(; n::Integer = default_nvar, kwargs...) = 1 * n + 0
+get_brownal_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_brownal_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_brownal_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_brownal_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_brownal_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_brownal_nls_nequ(; n::Integer = default_nvar, kwargs...) = 1 * n

src/Meta/broyden3d.jl

@@ -0,0 +1,26 @@
+broyden3d_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "broyden3d",
+  :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 => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+get_broyden3d_nvar(; n::Integer = default_nvar, kwargs...) = 1 * n + 0
+get_broyden3d_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden3d_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden3d_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden3d_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden3d_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden3d_nls_nequ(; n::Integer = default_nvar, kwargs...) = 1 * n

src/PureJuMP/argtrig.jl

@@ -0,0 +1,36 @@
+#
+#   Variable dimension trigonometric problem
+#   This problem is a sum of n least-squares groups, each of
+#   which has n+1 nonlinear elements.  Its Hessian matrix is dense.
+#
+#   Source: problem 26 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.
+#   Also problem 101 in
+#      A.R. Buckley,
+#      "Test functions for unconstrained minimization",
+#      TR 1989CS-3, Mathematics, statistics and computing centre,
+#      Dalhousie University, Halifax (CDN), 1989.
+#
+#   classification NOR2-AN-V-V
+
+export argtrig
+
+"Linear function with `n` parameters and `m` observations  - full rank"
+function argtrig(args...; n::Int = default_nvar, m::Int = 2n, kwargs...)
+  m < n && @warn("argtrig: must have m ≥ n")
+  m = max(m, n)
+
+  nlp = Model()
+
+  @variable(nlp, x[j = 1:n], start = 1 / n)
+
+  @NLobjective(
+    nlp,
+    Min,
+    n - sum(cos(x[j]) + j * (1 - cos(x[j])) - sin(x[j]) for j=1:n)
+  )
+
+  return nlp
+end

src/PureJuMP/bard.jl

@@ -0,0 +1,30 @@
+#   Bard problem in 3 variables.
+#   This function is a nonlinear least squares with 15 groups.
+#   Each group has a linear and a nonlinear element.
+#
+#   Source: Problem 8 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#16
+#
+#   classification SUR2-AN-3-0
+
+export bard
+
+"Linear function with `n` parameters and `m` observations  - full rank"
+function bard(args...; n::Int = default_nvar, m::Int = 2n, kwargs...)
+  y = Rational{Int}[0.14 0.18 0.22 0.25 0.29 0.32 0.35 0.39 0.37 0.58 0.73 0.16 1.34 2.10 4.39 ];
+  nlp = Model()
+
+  @variable(nlp, x[j = 1:3], start = 1.0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    0.5 * sum(y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3])) for i = 1:15)
+  )
+
+  return nlp
+end

src/PureJuMP/biggs5.jl

@@ -0,0 +1,35 @@
+#   Biggs problem in 5 variables.
+#   This function is a nonlinear least squares with 13 groups.  It is a
+#   variation on the biggs6 problem where the 6-th variable is fixed to 3.
+#
+#   Source: Inspited by problem 18 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.
+#   Also problem 74 in
+#      A.R. Buckley,
+#      "Test functions for unconstrained minimization",
+#      TR 1989CS-3, Mathematics, statistics and computing centre,
+#      Dalhousie University, Halifax (CDN), 1989.
+#
+# classification SXR2-AN-6-0
+export biggs5
+
+function biggs5(args...; n::Int = default_nvar, m::Int = 13, kwargs...)
+  m = max(6, m)
+  z = [i / 10 for i = 1:m]
+  y = [exp(-zi) - 5 * exp(-10 * zi) + 3 * exp(-4 * zi) for zi in z]
+  nlp = Model()
+  x0 = [1.0; 2.0; 1.0; 1.0; 1.0; 1.0]
+  @variable(nlp, x[i = 1:6], start = x0[i])
+  fix(x[6], 3)
+  @NLobjective(
+    nlp,
+    Min,
+    sum(
+      x[3] * exp(-x[1] * z[i]) - x[4] * exp(-x[2] * z[i]) + x[6] * exp(-x[5] * z[i]) - y[i] for
+      i = 1:m
+    )
+  )
+  return nlp
+end

src/PureJuMP/brownal.jl

@@ -0,0 +1,29 @@
+#   The Brown almost linear problem in variable dimension.  This is a nonlinear
+#   least-squares problems with n groups.
+#
+#   Source: Problem 27 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.
+#   Alsso problem 79 in 
+#      A.R. Buckley,
+#      "Test functions for unconstrained minimization",
+#      TR 1989CS-3, Mathematics, statistics and computing centre,
+#      Dalhousie University, Halifax (CDN), 1989.
+#
+export brownal
+
+"Brownbs Model"
+function brownal(args...; n::Int = default_nvar, kwargs...)
+  nlp = Model()
+
+  @variable(nlp, x[i = 1:n], start = 1/2)
+
+  @NLobjective(
+    nlp, 
+    Min, 
+    0.5 * sum((x[i] + sum(x[j] for j = 1:n) - (n + 1))^2 for i = 1:(n-1)) + 0.5 * (prod(x[j] for j = 1:n) - 1)^2
+  )
+
+  return nlp
+end