diff --git a/src/ADNLPProblems/auglag.jl b/src/ADNLPProblems/auglag.jl
new file mode 100644
index 00000000..5ea6648c
--- /dev/null
+++ b/src/ADNLPProblems/auglag.jl
@@ -0,0 +1,52 @@
+export auglag
+
+function auglag(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  λ₁ = T(-0.002008)
+  λ₂ = T(-0.001900)
+  λ₃ = T(-0.000261)
+
+  function f(x; n = length(x))
+    s = zero(T)
+    for i = 1:n
+      if mod(i, 5) == 0
+        prod_term = one(T)
+        sum_sq = zero(T)
+        for j = 1:5
+          idx = i + 1 - j
+          if 1 <= idx <= n
+            prod_term *= x[idx]
+            sum_sq += x[idx]^2
+          end
+        end
+        s += exp(prod_term) + 10 * (sum_sq - 10 - λ₁)^2
+
+        if i >= 4
+          s += 10 * (x[i - 3] * x[i - 2] - 5 * x[i - 1] * x[i] - λ₂)^2
+        end
+
+        if i >= 4
+          s += 10 * (x[i - 4]^3 + x[i - 3]^3 + 1 - λ₃)^2
+        end
+      end
+    end
+    return s
+  end
+
+  x0 = zeros(T, n)
+  for i = 1:n
+    m = mod(i, 5)
+    if m == 1
+      x0[i] = i <= 2 ? -2 : -1
+    elseif m == 2
+      x0[i] = i <= 2 ? 2 : -1
+    elseif m == 3
+      x0[i] = 2
+    elseif m == 4
+      x0[i] = -1
+    else
+      x0[i] = -1
+    end
+  end
+
+  return ADNLPModels.ADNLPModel(f, x0, name = "auglag"; kwargs...)
+end
diff --git a/src/ADNLPProblems/browngen1.jl b/src/ADNLPProblems/browngen1.jl
new file mode 100644
index 00000000..8516338d
--- /dev/null
+++ b/src/ADNLPProblems/browngen1.jl
@@ -0,0 +1,14 @@
+export browngen1
+
+function browngen1(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  n = max(2, n)
+  function f(x; n = length(x))
+    s = zero(T)
+    @inbounds for i = 2:n
+      s += (x[i - 1] - 3)^2 + (x[i - 1] - x[i])^2 + exp(20 * (x[i - 1] - x[i]))
+    end
+    return s
+  end
+  x0 = [isodd(i) ? zero(T) : -one(T) for i = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "browngen1"; kwargs...)
+end
diff --git a/src/ADNLPProblems/browngen2.jl b/src/ADNLPProblems/browngen2.jl
new file mode 100644
index 00000000..da7789ad
--- /dev/null
+++ b/src/ADNLPProblems/browngen2.jl
@@ -0,0 +1,14 @@
+export browngen2
+
+function browngen2(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  n = max(2, n)
+  function f(x; n = length(x))
+    s = zero(T)
+    @inbounds for i = 2:n
+      s += (x[i - 1]^2)^(x[i]^2 + 1) + (x[i]^2)^(x[i - 1]^2 + 1)
+    end
+    return s
+  end
+  x0 = [isodd(i) ? -one(T) : one(T) for i = 1:n]
+  return ADNLPModels.ADNLPModel(f, x0, name = "browngen2"; kwargs...)
+end
diff --git a/src/ADNLPProblems/broyden7d.jl b/src/ADNLPProblems/broyden7d.jl
new file mode 100644
index 00000000..454dc9fb
--- /dev/null
+++ b/src/ADNLPProblems/broyden7d.jl
@@ -0,0 +1,48 @@
+export broyden7d
+
+function broyden7d(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return broyden7d(Val(model); kwargs...)
+end
+
+function broyden7d(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  p = 7 // 3
+  function f(x; n = length(x), p = p)
+    x0 = zero(T)
+    xn1 = zero(T)
+    s = zero(T)
+    s += abs((3 - 2 * x[1]) * x[1] - x0 - x[2] + 1)^p
+    for i = 2:(n - 1)
+      s += abs((3 - 2 * x[i]) * x[i] - x[i - 1] - x[i + 1] + 1)^p
+    end
+    s += abs((3 - 2 * x[n]) * x[n] - x[n - 1] - xn1 + 1)^p
+    nh = div(n, 2)
+    for i = 1:nh
+      s += abs(x[i] + x[i + nh])^p
+    end
+    return s
+  end
+  x0 = fill(-one(T), n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "broyden7d"; kwargs...)
+end
+
+function broyden7d(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  x0 = fill(-one(T), n)
+  function F!(r, x; n = length(x))
+    p = 7 // 6
+    nh = div(n, 2)
+    @inbounds begin
+      r[1] = abs((3 - 2 * x[1]) * x[1] - zero(T) - x[2] + one(T))^p
+      for i = 2:(n - 1)
+        r[i] = abs((3 - 2 * x[i]) * x[i] - x[i - 1] - x[i + 1] + one(T))^p
+      end
+      r[n] = abs((3 - 2 * x[n]) * x[n] - x[n - 1] - zero(T) + one(T))^p
+      for i = 1:nh
+        r[n + i] = abs(x[i] + x[i + nh])^p
+      end
+    end
+    return r
+  end
+  nequ = n + div(n, 2)
+  return ADNLPModels.ADNLSModel!(F!, x0, nequ, name = "broyden7d-nls"; kwargs...)
+end
diff --git a/src/ADNLPProblems/chainwoo.jl b/src/ADNLPProblems/chainwoo.jl
index e7d93586..9d1520fe 100644
--- a/src/ADNLPProblems/chainwoo.jl
+++ b/src/ADNLPProblems/chainwoo.jl
@@ -1,6 +1,11 @@
 export chainwoo
 
-function chainwoo(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+function chainwoo(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return chainwoo(Val(model); kwargs...)
+end
+
+function chainwoo(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   (n % 4 == 0) || @warn("chainwoo: number of variables adjusted to be a multiple of 4")
   n = 4 * max(1, div(n, 4))
   function f(x; n = length(x))
@@ -16,3 +21,26 @@ function chainwoo(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) w
   x0 = vcat([-3, -1, -3, -1], -2 * ones(T, n - 4))
   return ADNLPModels.ADNLPModel(f, x0, name = "chainwoo"; kwargs...)
 end
+
+function chainwoo(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  (n % 4 == 0) || @warn("chainwoo: number of variables adjusted to be a multiple of 4")
+  n = 4 * max(1, div(n, 4))
+  function F!(r, x; n = length(x))
+    nb = div(n, 2) - 1
+    r[1] = 1
+    idx = 2
+    @inbounds for i = 1:nb
+      r[idx] = 10 * (x[2 * i] - x[2 * i - 1]^2)
+      r[idx + 1] = 1 - x[2 * i - 1]
+      r[idx + 2] = T(sqrt(90)) * (x[2 * i + 2] - x[2 * i + 1]^2)
+      r[idx + 3] = 1 - x[2 * i + 1]
+      r[idx + 4] = T(sqrt(10)) * (x[2 * i] + x[2 * i + 2] - 2)
+      r[idx + 5] = (x[2 * i] - x[2 * i + 2]) / T(sqrt(10))
+      idx += 6
+    end
+    return r
+  end
+  nequ = 1 + 6 * (div(n, 2) - 1)
+  x0 = vcat([-3, -1, -3, -1], -2 * ones(T, n - 4))
+  return ADNLPModels.ADNLSModel!(F!, x0, nequ, name = "chainwoo-nls"; kwargs...)
+end
diff --git a/src/ADNLPProblems/cragglvy2.jl b/src/ADNLPProblems/cragglvy2.jl
index 0411752d..5fb26059 100644
--- a/src/ADNLPProblems/cragglvy2.jl
+++ b/src/ADNLPProblems/cragglvy2.jl
@@ -1,6 +1,11 @@
 export cragglvy2
 
-function cragglvy2(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+function cragglvy2(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return cragglvy2(Val(model); kwargs...)
+end
+
+function cragglvy2(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   n < 2 && @warn("cragglvy2: number of variables must be ≥ 2")
   n = max(2, n)
   function f(x; n = length(x))
@@ -15,3 +20,21 @@ function cragglvy2(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...)
   x0 = vcat(1, 2 * ones(T, n - 1))
   return ADNLPModels.ADNLPModel(f, x0, name = "cragglvy2"; kwargs...)
 end
+
+function cragglvy2(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  n < 2 && @warn("cragglvy2: number of variables must be ≥ 2")
+  n = max(2, n)
+  function F!(r, x; n = length(x))
+    for i = 1:(div(n, 2) - 1)
+      r[5 * (i - 1) + 1] = (exp(x[2 * i - 1]) - x[2 * i])^2
+      r[5 * (i - 1) + 2] = 10 * (x[2 * i] - x[2 * i + 1])^3
+      r[5 * (i - 1) + 3] = (tan(x[2 * i + 1] - x[2 * i + 2]))^2
+      r[5 * (i - 1) + 4] = x[2 * i - 1]^4
+      r[5 * (i - 1) + 5] = x[2 * i + 2] - 1
+    end
+    return r
+  end
+  nequ = 5 * (div(n, 2) - 1)
+  x0 = vcat(T(1), T(2) * ones(T, n - 1))
+  return ADNLPModels.ADNLSModel!(F!, x0, nequ, name = "cragglvy2-nls"; kwargs...)
+end
diff --git a/src/ADNLPProblems/genbroydenb.jl b/src/ADNLPProblems/genbroydenb.jl
new file mode 100644
index 00000000..be50d1de
--- /dev/null
+++ b/src/ADNLPProblems/genbroydenb.jl
@@ -0,0 +1,47 @@
+export genbroydenb
+
+function genbroydenb(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return genbroydenb(Val(model); kwargs...)
+end
+
+function genbroydenb(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  p = 7 // 3
+  function f(x; n = length(x))
+    s = zero(T)
+    for i = 1:n
+      diag = (2 + 5 * x[i]^2) * x[i] + 1
+      neigh = zero(T)
+      @inbounds for j = max(1, i - 5):min(n, i + 1)
+        if j != i
+          neigh += x[j] * (1 + x[j])
+        end
+      end
+      s += abs(diag + neigh)^p
+    end
+    return s
+  end
+  x0 = fill(-one(T), n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "genbroydenb", minimize = true; kwargs...)
+end
+
+function genbroydenb(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  p = 7 // 6
+  function F!(r, x)
+    m = length(x)
+    @inbounds for i = 1:m
+      diag = (2 + 5 * x[i]^2) * x[i] + 1
+      neigh = zero(T)
+      for j = max(1, i - 5):min(m, i + 1)
+        if j != i
+          neigh += x[j] * (1 + x[j])
+        end
+      end
+      z = diag + neigh
+      r[i] = abs(z)^(p)
+    end
+    return r
+  end
+x0 = fill(-one(T), n)
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "genbroydenb-nls"; kwargs...)
+end
diff --git a/src/ADNLPProblems/genbroydentri.jl b/src/ADNLPProblems/genbroydentri.jl
new file mode 100644
index 00000000..0cf95c19
--- /dev/null
+++ b/src/ADNLPProblems/genbroydentri.jl
@@ -0,0 +1,50 @@
+export genbroydentri
+
+function genbroydentri(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return genbroydentri(Val(model); kwargs...)
+end
+
+function genbroydentri(
+  ::Val{:nlp};
+  n::Int = default_nvar,
+  type::Type{T} = Float64,
+  kwargs...,
+) where {T}
+  p = 7 // 3
+  function f(x; n = length(x))
+    x0 = zero(T)
+    xn1 = zero(T)
+    s = abs((3 - 2 * x[1]) * x[1] - x0 - x[2] + 1)^p
+    for i = 2:(n - 1)
+      s += abs((3 - 2 * x[i]) * x[i] - x[i - 1] - x[i + 1] + 1)^p
+    end
+    s += abs((3 - 2 * x[n]) * x[n] - x[n - 1] - xn1 + 1)^p
+    return s
+  end
+  x0 = fill(-one(T), n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "genbroydentri"; kwargs...)
+end
+
+function genbroydentri(
+  ::Val{:nls};
+  n::Int = default_nvar,
+  type::Type{T} = Float64,
+  kwargs...,
+) where {T}
+  p = 7 // 6
+  x0 = fill(-one(T), n)
+  function F!(r, x)
+    x0_val = zero(T)
+    xn1_val = zero(T)
+    @inbounds begin
+      r[1] = abs((3 - 2 * x[1]) * x[1] - x0_val - x[2] + 1)^p
+      for i = 2:(n - 1)
+        r[i] = abs((3 - 2 * x[i]) * x[i] - x[i - 1] - x[i + 1] + 1)^p
+      end
+      r[n] = abs((3 - 2 * x[n]) * x[n] - x[n - 1] - xn1_val + 1)^p
+    end
+    return r
+  end
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "genbroydentri-nls"; kwargs...)
+end
diff --git a/src/ADNLPProblems/genrose.jl b/src/ADNLPProblems/genrose.jl
index 9448d2f6..d48c85a6 100644
--- a/src/ADNLPProblems/genrose.jl
+++ b/src/ADNLPProblems/genrose.jl
@@ -1,6 +1,11 @@
 export genrose, rosenbrock
 
-function genrose(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+function genrose(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return genrose(Val(model); kwargs...)
+end
+
+function genrose(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   n < 2 && @warn("genrose: number of variables must be ≥ 2")
   n = max(2, n)
   function f(x; n = length(x))
@@ -12,5 +17,22 @@ function genrose(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
   return ADNLPModels.ADNLPModel(f, x0, name = "genrose"; kwargs...)
 end
 
+function genrose(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  n = max(2, n)
+  nequ = 2 * (n - 1) + 1
+  function F!(r, x; n = length(x))
+    @inbounds begin
+      r[1] = 1
+      for i = 1:(n - 1)
+        r[i + 1] = 10 * (x[i + 1] - x[i]^2)
+        r[i + n] = x[i] - 1
+      end
+    end
+    return r
+  end
+  x0 = T.([i / (n + 1) for i = 1:n])
+  return ADNLPModels.ADNLSModel!(F!, x0, nequ, name = "genrose-nls"; kwargs...)
+end
+
 rosenbrock(args...; kwargs...) =
   genrose(args..., n = 2, name = "rosenbrock"; delete!(Dict(kwargs), :n)...)
diff --git a/src/ADNLPProblems/nazareth.jl b/src/ADNLPProblems/nazareth.jl
new file mode 100644
index 00000000..04ae25bc
--- /dev/null
+++ b/src/ADNLPProblems/nazareth.jl
@@ -0,0 +1,85 @@
+export nazareth
+
+function nazareth(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return nazareth(Val(model); kwargs...)
+end
+
+function nazareth(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  nh = div(n, 2)
+  neighbors = Vector{Vector{Int}}(undef, n)
+  a_row = Vector{Vector{T}}(undef, n)
+  b_row = Vector{Vector{T}}(undef, n)
+  for i = 1:n
+    lo = max(1, i - 2)
+    hi = min(n, i + 2)
+    neigh = collect(lo:hi)
+    j1 = i - nh
+    j2 = i + nh
+    for j in (j1, j2)
+      if 1 <= j <= n && !(j >= lo && j <= hi)
+        push!(neigh, j)
+      end
+    end
+    neighbors[i] = neigh
+    a_row[i] = [5 * (1 + mod(i, 5) + mod(j, 5)) for j in neigh]
+    b_row[i] = [(i + j) / 10 for j in neigh]
+  end
+
+  function f(x; n = length(x))
+    s = zero(T)
+    for i = 1:n
+      sumtrig = zero(T)
+      neigh = neighbors[i]
+      ai = a_row[i]
+      bi = b_row[i]
+      @inbounds for k = 1:length(neigh)
+        j = neigh[k]
+        sumtrig += ai[k] * sin(x[j]) + bi[k] * cos(x[j])
+      end
+      s += (n + i - sumtrig)^2
+    end
+    return s / n
+  end
+  x0 = fill(one(T) / n, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "nazareth", minimize = true; kwargs...)
+end
+
+function nazareth(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  nh = div(n, 2)
+  neighbors = Vector{Vector{Int}}(undef, n)
+  a_row = Vector{Vector{T}}(undef, n)
+  b_row = Vector{Vector{T}}(undef, n)
+  for i = 1:n
+    lo = max(1, i - 2)
+    hi = min(n, i + 2)
+    neigh = collect(lo:hi)
+    j1 = i - nh
+    j2 = i + nh
+    for j in (j1, j2)
+      if 1 <= j <= n && !(j >= lo && j <= hi)
+        push!(neigh, j)
+      end
+    end
+    neighbors[i] = neigh
+    a_row[i] = [5 * (1 + mod(i, 5) + mod(j, 5)) for j in neigh]
+    b_row[i] = [(i + j) / 10 for j in neigh]
+  end
+
+  x0 = fill(one(T) / n, n)
+  function F!(r, x)
+    @inbounds for i = 1:n
+      sumtrig = zero(T)
+      neigh = neighbors[i]
+      ai = a_row[i]
+      bi = b_row[i]
+      for k = 1:length(neigh)
+        j = neigh[k]
+        sumtrig += ai[k] * sin(x[j]) + bi[k] * cos(x[j])
+      end
+      r[i] = (n + i - sumtrig) / sqrt(T(n))
+    end
+    return r
+  end
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "nazareth"; kwargs...)
+end
diff --git a/src/ADNLPProblems/powellsg.jl b/src/ADNLPProblems/powellsg.jl
index ee0c09c5..38ac7db6 100644
--- a/src/ADNLPProblems/powellsg.jl
+++ b/src/ADNLPProblems/powellsg.jl
@@ -1,6 +1,11 @@
 export powellsg
 
-function powellsg(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+function powellsg(; use_nls::Bool = false, kwargs...)
+  model = use_nls ? :nls : :nlp
+  return powellsg(Val(model); kwargs...)
+end
+
+function powellsg(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   (n % 4 == 0) || @warn("powellsg: number of variables adjusted to be a multiple of 4")
   n = 4 * max(1, div(n, 4))  # number of variables adjusted to be a multiple of 4
   function f(x; n = length(x))
@@ -17,3 +22,22 @@ function powellsg(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) w
   x0[4 * (collect(1:div(n, 4)))] .= 1
   return ADNLPModels.ADNLPModel(f, x0, name = "powellsg"; kwargs...)
 end
+
+function powellsg(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  (n % 4 == 0) || @warn("powellsg: number of variables adjusted to be a multiple of 4")
+  n = 4 * max(1, div(n, 4))
+  function F!(r, x; n = length(x))
+    @inbounds for j = 1:4:n
+      r[j] = x[j] + 10 * x[j + 1]
+      r[j + 1] = T(sqrt(5)) * (x[j + 2] - x[j + 3])
+      r[j + 2] = (x[j + 1] - 2 * x[j + 2])^2
+      r[j + 3] = T(sqrt(10)) * (x[j] - x[j + 3])^2
+    end
+    return r
+  end
+  x0 = zeros(T, n)
+  x0[4 * (collect(1:div(n, 4))) .- 3] .= 3
+  x0[4 * (collect(1:div(n, 4))) .- 2] .= -1
+  x0[4 * (collect(1:div(n, 4)))] .= 1
+  return ADNLPModels.ADNLSModel!(F!, x0, n, name = "powellsg-nls"; kwargs...)
+end
diff --git a/src/Meta/auglag.jl b/src/Meta/auglag.jl
new file mode 100644
index 00000000..75f7e5bc
--- /dev/null
+++ b/src/Meta/auglag.jl
@@ -0,0 +1,27 @@
+auglag_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "auglag",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_auglag_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_auglag_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_auglag_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_auglag_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_auglag_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_auglag_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_auglag_nls_nequ(; n::Integer = default_nvar, kwargs...) = 0
diff --git a/src/Meta/browngen1.jl b/src/Meta/browngen1.jl
new file mode 100644
index 00000000..1691c13f
--- /dev/null
+++ b/src/Meta/browngen1.jl
@@ -0,0 +1,27 @@
+browngen1_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "browngen1",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_browngen1_nvar(; n::Integer = default_nvar, kwargs...) = max(n, 2)
+get_browngen1_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen1_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen1_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen1_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen1_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen1_nls_nequ(; n::Integer = default_nvar, kwargs...) = 0
diff --git a/src/Meta/browngen2.jl b/src/Meta/browngen2.jl
new file mode 100644
index 00000000..35ba4d17
--- /dev/null
+++ b/src/Meta/browngen2.jl
@@ -0,0 +1,27 @@
+browngen2_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "browngen2",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_browngen2_nvar(; n::Integer = default_nvar, kwargs...) = max(2, n)
+get_browngen2_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen2_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen2_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen2_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen2_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_browngen2_nls_nequ(; n::Integer = default_nvar, kwargs...) = 0
diff --git a/src/Meta/broyden7d.jl b/src/Meta/broyden7d.jl
new file mode 100644
index 00000000..e257af74
--- /dev/null
+++ b/src/Meta/broyden7d.jl
@@ -0,0 +1,27 @@
+broyden7d_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "broyden7d",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_broyden7d_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_broyden7d_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden7d_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden7d_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden7d_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden7d_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_broyden7d_nls_nequ(; n::Integer = default_nvar, kwargs...) = n + div(n, 2)
diff --git a/src/Meta/chainwoo.jl b/src/Meta/chainwoo.jl
index bd6a2ccd..63036f1f 100644
--- a/src/Meta/chainwoo.jl
+++ b/src/Meta/chainwoo.jl
@@ -9,7 +9,7 @@ chainwoo_meta = Dict(
   :has_inequalities_only => false,
   :has_bounds => false,
   :has_fixed_variables => false,
-  :objtype => :other,
+  :objtype => :least_squares,
   :contype => :unconstrained,
   :best_known_lower_bound => -Inf,
   :best_known_upper_bound => 371954.1,
@@ -23,3 +23,4 @@ get_chainwoo_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_chainwoo_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_chainwoo_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_chainwoo_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_chainwoo_nls_nequ(; n::Integer = default_nvar, kwargs...) = 1 + 6 * (div(n, 2) - 1)
diff --git a/src/Meta/cragglvy2.jl b/src/Meta/cragglvy2.jl
index ab90537e..194bfca9 100644
--- a/src/Meta/cragglvy2.jl
+++ b/src/Meta/cragglvy2.jl
@@ -9,7 +9,7 @@ cragglvy2_meta = Dict(
   :has_inequalities_only => false,
   :has_bounds => false,
   :has_fixed_variables => false,
-  :objtype => :other,
+  :objtype => :least_squares,
   :contype => :unconstrained,
   :best_known_lower_bound => -Inf,
   :best_known_upper_bound => 52823.07152952862,
@@ -17,9 +17,11 @@ cragglvy2_meta = Dict(
   :defined_everywhere => missing,
   :origin => :unknown,
 )
+
 get_cragglvy2_nvar(; n::Integer = default_nvar, kwargs...) = 1 * n + 0
 get_cragglvy2_ncon(; n::Integer = default_nvar, kwargs...) = 0
 get_cragglvy2_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_cragglvy2_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_cragglvy2_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_cragglvy2_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_cragglvy2_nls_nequ(; n::Integer = default_nvar, kwargs...) = 5 * (div(n, 2) - 1)
diff --git a/src/Meta/genbroydenb.jl b/src/Meta/genbroydenb.jl
new file mode 100644
index 00000000..2ecb87ad
--- /dev/null
+++ b/src/Meta/genbroydenb.jl
@@ -0,0 +1,27 @@
+genbroydenb_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "genbroydenb",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_genbroydenb_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_genbroydenb_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydenb_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydenb_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydenb_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydenb_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydenb_nls_nequ(; n::Integer = default_nvar, kwargs...) = n
diff --git a/src/Meta/genbroydentri.jl b/src/Meta/genbroydentri.jl
new file mode 100644
index 00000000..4ee3003d
--- /dev/null
+++ b/src/Meta/genbroydentri.jl
@@ -0,0 +1,27 @@
+genbroydentri_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "genbroydentri",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_genbroydentri_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_genbroydentri_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydentri_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydentri_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydentri_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydentri_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_genbroydentri_nls_nequ(; n::Integer = default_nvar, kwargs...) = n
diff --git a/src/Meta/genrose.jl b/src/Meta/genrose.jl
index de76deb4..53fe1bc2 100644
--- a/src/Meta/genrose.jl
+++ b/src/Meta/genrose.jl
@@ -9,7 +9,7 @@ genrose_meta = Dict(
   :has_inequalities_only => false,
   :has_bounds => false,
   :has_fixed_variables => false,
-  :objtype => :other,
+  :objtype => :least_squares,
   :contype => :unconstrained,
   :best_known_lower_bound => -Inf,
   :best_known_upper_bound => 405.1064193957891,
@@ -23,3 +23,4 @@ get_genrose_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_genrose_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_genrose_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_genrose_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_genrose_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * (n - 1) + 1
diff --git a/src/Meta/nazareth.jl b/src/Meta/nazareth.jl
new file mode 100644
index 00000000..1efd0599
--- /dev/null
+++ b/src/Meta/nazareth.jl
@@ -0,0 +1,27 @@
+nazareth_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "nazareth",
+  :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 => missing,
+  :defined_everywhere => missing,
+  :origin => :literature,
+)
+
+get_nazareth_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_nazareth_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_nazareth_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_nazareth_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_nazareth_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_nazareth_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_nazareth_nls_nequ(; n::Integer = default_nvar, kwargs...) = n
diff --git a/src/Meta/powellsg.jl b/src/Meta/powellsg.jl
index 331e3a47..51b2de14 100644
--- a/src/Meta/powellsg.jl
+++ b/src/Meta/powellsg.jl
@@ -9,7 +9,7 @@ powellsg_meta = Dict(
   :has_inequalities_only => false,
   :has_bounds => false,
   :has_fixed_variables => false,
-  :objtype => :other,
+  :objtype => :least_squares,
   :contype => :unconstrained,
   :best_known_lower_bound => -Inf,
   :best_known_upper_bound => 5375.0,
@@ -23,3 +23,4 @@ get_powellsg_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_powellsg_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_powellsg_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_powellsg_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_powellsg_nls_nequ(; n::Integer = default_nvar, kwargs...) = 4 * max(1, div(n, 4))
diff --git a/src/Meta/rosenbrock.jl b/src/Meta/rosenbrock.jl
index 32a08387..e39be54a 100644
--- a/src/Meta/rosenbrock.jl
+++ b/src/Meta/rosenbrock.jl
@@ -9,7 +9,7 @@ rosenbrock_meta = Dict(
   :has_inequalities_only => false,
   :has_bounds => false,
   :has_fixed_variables => false,
-  :objtype => :other,
+  :objtype => :least_squares,
   :contype => :unconstrained,
   :best_known_lower_bound => -Inf,
   :best_known_upper_bound => 32.308641975308646,
@@ -23,3 +23,4 @@ get_rosenbrock_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_rosenbrock_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_rosenbrock_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_rosenbrock_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_rosenbrock_nls_nequ(; n::Integer = default_nvar, kwargs...) = 3
diff --git a/src/PureJuMP/auglag.jl b/src/PureJuMP/auglag.jl
new file mode 100644
index 00000000..8508767f
--- /dev/null
+++ b/src/PureJuMP/auglag.jl
@@ -0,0 +1,52 @@
+# Augmented Lagrangian function
+#
+#   Problem 11 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 auglag
+
+function auglag(; n::Int = default_nvar)
+  λ₁ = -0.002008
+  λ₂ = -0.001900
+  λ₃ = -0.000261
+
+  nlp = Model()
+  @variable(nlp, x[1:n])
+
+  for i = 1:n
+    m = mod(i, 5)
+    if m == 1
+      set_start_value(x[i], i <= 2 ? -2.0 : -1.0)
+    elseif m == 2
+      set_start_value(x[i], i <= 2 ? 2.0 : -1.0)
+    elseif m == 3
+      set_start_value(x[i], 2.0)
+    elseif m == 4
+      set_start_value(x[i], -1.0)
+    else
+      set_start_value(x[i], -1.0)
+    end
+  end
+
+  # Build objective only for i where mod(i, 5) == 0 and i >= 5
+  indices = [i for i = 5:n if mod(i, 5) == 0]
+
+  @objective(
+    nlp,
+    Min,
+    sum(
+      exp(prod(x[i + 1 - j] for j = 1:5)) +
+      10 * (sum(x[i + 1 - j]^2 for j = 1:5) - 10 - λ₁)^2 +
+      10 * (x[i - 3]*x[i - 2] - 5*x[i - 1]*x[i] - λ₂)^2 +
+      10 * (x[i - 4]^3 + x[i - 3]^3 + 1 - λ₃)^2 for i in indices
+    )
+  )
+
+  return nlp
+end
diff --git a/src/PureJuMP/browngen1.jl b/src/PureJuMP/browngen1.jl
new file mode 100644
index 00000000..a2af8afa
--- /dev/null
+++ b/src/PureJuMP/browngen1.jl
@@ -0,0 +1,27 @@
+# Generalization of the Brown function 1
+#
+#   Problem 12 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 browngen1
+
+function browngen1(; n::Int = default_nvar)
+  nlp = Model()
+  n = max(2, n)
+  @variable(nlp, x[1:n])
+  for i = 1:n
+    set_start_value(x[i], isodd(i) ? 0.0 : -1.0)
+  end
+
+  @objective(
+    nlp,
+    Min,
+    sum((x[i - 1] - 3)^2 + (x[i - 1] - x[i])^2 + exp(20 * (x[i - 1] - x[i])) for i = 2:n)
+  )
+  return nlp
+end
diff --git a/src/PureJuMP/browngen2.jl b/src/PureJuMP/browngen2.jl
new file mode 100644
index 00000000..d779cc6a
--- /dev/null
+++ b/src/PureJuMP/browngen2.jl
@@ -0,0 +1,23 @@
+# Generalization of the Brown function 2
+#
+#   Problem 13 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 browngen2
+
+function browngen2(; n::Int = default_nvar)
+  nlp = Model()
+  n = max(2, n)
+  @variable(nlp, x[1:n])
+  for i = 1:n
+    set_start_value(x[i], isodd(i) ? -1.0 : 1.0)
+  end
+
+  @objective(nlp, Min, sum((x[i - 1]^2)^(x[i]^2 + 1) + (x[i]^2)^(x[i - 1]^2 + 1) for i = 2:n))
+  return nlp
+end
diff --git a/src/PureJuMP/broyden7d.jl b/src/PureJuMP/broyden7d.jl
new file mode 100644
index 00000000..60c8d49a
--- /dev/null
+++ b/src/PureJuMP/broyden7d.jl
@@ -0,0 +1,27 @@
+# Seven diagonal generalization of the Broyden tridiagonal function
+#
+#   Problem 7 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 broyden7d
+
+function broyden7d(; n::Int = default_nvar)
+  p = 7 / 3
+  nh = div(n, 2)
+  nlp = Model()
+  @variable(nlp, x[1:n], start = -1.0)
+  @objective(
+    nlp,
+    Min,
+    abs((3 - 2 * x[1]) * x[1] - 0 - x[2] + 1)^p +
+    sum(abs((3 - 2 * x[i]) * x[i] - x[i - 1] - x[i + 1] + 1)^p for i = 2:(n - 1)) +
+    abs((3 - 2 * x[n]) * x[n] - x[n - 1] - 0 + 1)^p +
+    sum(abs(x[i] + x[i + nh])^p for i = 1:nh)
+  )
+  return nlp
+end
diff --git a/src/PureJuMP/genbroydenb.jl b/src/PureJuMP/genbroydenb.jl
new file mode 100644
index 00000000..483478b7
--- /dev/null
+++ b/src/PureJuMP/genbroydenb.jl
@@ -0,0 +1,29 @@
+# Generalized Broyden banded function
+#
+#   Problem 6 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 genbroydenb
+
+function genbroydenb(; n::Int = default_nvar)
+  p = 7 / 3
+  nlp = Model()
+  @variable(nlp, x[1:n], start = -1.0)
+  @objective(
+    nlp,
+    Min,
+    sum(
+      abs(
+        (2 + 5 * x[i]^2) * x[i] +
+        1 +
+        sum(x[j] * (1 + x[j]) for j = max(1, i - 5):min(n, i + 1) if j != i),
+      )^p for i = 1:n
+    )
+  )
+  return nlp
+end
diff --git a/src/PureJuMP/genbroydentri.jl b/src/PureJuMP/genbroydentri.jl
new file mode 100644
index 00000000..9abdf6e7
--- /dev/null
+++ b/src/PureJuMP/genbroydentri.jl
@@ -0,0 +1,25 @@
+# Generalized Broyden Tridiagonal Function
+#
+#   Problem 5 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 genbroydentri
+
+function genbroydentri(; n::Int = default_nvar)
+  p = 7 / 3
+  nlp = Model()
+  @variable(nlp, x[1:n], start = -1.0)
+  @objective(
+    nlp,
+    Min,
+    abs((3 - 2 * x[1]) * x[1] - 0 - x[2] + 1)^p +
+    sum(abs((3 - 2 * x[i]) * x[i] - x[i - 1] - x[i + 1] + 1)^p for i = 2:(n - 1)) +
+    abs((3 - 2 * x[n]) * x[n] - x[n - 1] - 0 + 1)^p
+  )
+  return nlp
+end
diff --git a/src/PureJuMP/nazareth.jl b/src/PureJuMP/nazareth.jl
new file mode 100644
index 00000000..f719ac16
--- /dev/null
+++ b/src/PureJuMP/nazareth.jl
@@ -0,0 +1,45 @@
+# Sparse modification of the Nazareth trigonometric function
+#
+#   Problem 8 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 nazareth
+
+function nazareth(; n::Int = default_nvar)
+  nh = div(n, 2)
+
+  nlp = Model()
+  @variable(nlp, x[1:n], start = 1 / n)
+
+  @objective(nlp, Min, sum((
+    begin
+      lo = max(1, i - 2)
+      hi = min(n, i + 2)
+
+      sumtrig = 0
+      for j = lo:hi
+        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+        bij = (i + j) / 10
+        sumtrig += aij * sin(x[j]) + bij * cos(x[j])
+      end
+
+      j1 = i - nh
+      j2 = i + nh
+      for j in (j1, j2)
+        if 1 <= j <= n && (j < lo || j > hi)
+          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+          bij = (i + j) / 10
+          sumtrig += aij * sin(x[j]) + bij * cos(x[j])
+        end
+      end
+
+      (n + i - sumtrig)^2
+    end
+  ) for i = 1:n) / n)
+  return nlp
+end