diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index 190eab5..08fe501 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -7,6 +7,7 @@ mutable struct MathOptNLPModel <: AbstractNLPModel{Float64, Vector{Float64}}
   quadcon::QuadraticConstraints
   nlcon::NonLinearStructure
   λ::Vector{Float64}
+  hv::Vector{Float64}
   obj::Objective
   counters::Counters
 end
@@ -34,7 +35,8 @@ function nlp_model(moimodel::MOI.ModelLike; hessian::Bool = true, name::String =
 
   nlp_data = _nlp_block(moimodel)
   nnln, nlcon, nl_lcon, nl_ucon = parser_NL(nlp_data, hessian = hessian)
-  λ = zeros(nnln)  # Lagrange multipliers for hess_coord! and hprod! without y
+  λ = zeros(Float64, nnln)  # Lagrange multipliers for hess_coord! and hprod! without y
+  hv = zeros(Float64, nvar)  # workspace for ghjvprod!
 
   if nlp_data.has_objective
     obj = Objective("NONLINEAR", 0.0, spzeros(Float64, nvar), COO(), 0)
@@ -67,7 +69,7 @@ function nlp_model(moimodel::MOI.ModelLike; hessian::Bool = true, name::String =
     name = name,
   )
 
-  return MathOptNLPModel(meta, nlp_data.evaluator, lincon, quadcon, nlcon, λ, obj, Counters()),
+  return MathOptNLPModel(meta, nlp_data.evaluator, lincon, quadcon, nlcon, λ, hv, obj, Counters()),
   index_map
 end
 
@@ -349,6 +351,38 @@ function NLPModels.hess_coord!(
   return vals
 end
 
+function NLPModels.jth_hess_coord!(
+  nlp::MathOptNLPModel,
+  x::AbstractVector,
+  j::Integer,
+  vals::AbstractVector,
+)
+  increment!(nlp, :neval_jhess)
+  @rangecheck 1 nlp.meta.ncon j
+  vals .= 0.0
+  if nlp.meta.nlin + 1 ≤ j ≤ nlp.meta.nlin + nlp.quadcon.nquad
+    index = nlp.obj.nnzh
+    for i = 1:(nlp.quadcon.nquad)
+      qcon = nlp.quadcon.constraints[i]
+      if j == nlp.meta.nlin + i
+        view(vals, (index + 1):(index + qcon.nnzh)) .= qcon.A.vals
+      end
+      index += qcon.nnzh
+    end
+  elseif nlp.meta.nlin + nlp.quadcon.nquad + 1 ≤ j ≤ nlp.meta.ncon
+    nlp.λ[j - nlp.meta.nlin - nlp.quadcon.nquad] = 1.0
+    MOI.eval_hessian_lagrangian(
+      nlp.eval,
+      view(vals, (nlp.obj.nnzh + nlp.quadcon.nnzh + 1):(nlp.meta.nnzh)),
+      x,
+      0.0,
+      nlp.λ,
+    )
+    nlp.λ[j - nlp.meta.nlin - nlp.quadcon.nquad] = 0.0
+  end
+  return vals
+end
+
 function NLPModels.hprod!(
   nlp::MathOptNLPModel,
   x::AbstractVector,
@@ -413,3 +447,45 @@ function NLPModels.hprod!(
   end
   return hv
 end
+
+function NLPModels.jth_hprod!(
+  nlp::MathOptNLPModel,
+  x::AbstractVector,
+  v::AbstractVector,
+  j::Integer,
+  hv::AbstractVector,
+)
+  increment!(nlp, :neval_jhprod)
+  @rangecheck 1 nlp.meta.ncon j
+  hv .= 0.0
+  if nlp.meta.nlin + 1 ≤ j ≤ nlp.meta.nlin + nlp.quadcon.nquad
+    qcon = nlp.quadcon.constraints[j - nlp.meta.nlin]
+    coo_sym_add_mul!(qcon.A.rows, qcon.A.cols, qcon.A.vals, v, hv, 1.0)
+  elseif nlp.meta.nlin + nlp.quadcon.nquad + 1 ≤ j ≤ nlp.meta.ncon
+    nlp.λ[j - nlp.meta.nlin - nlp.quadcon.nquad] = 1.0
+    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, 0.0, nlp.λ)
+    nlp.λ[j - nlp.meta.nlin - nlp.quadcon.nquad] = 0.0
+  end
+  return hv
+end
+
+function NLPModels.ghjvprod!(
+  nlp::MathOptNLPModel,
+  x::AbstractVector,
+  g::AbstractVector,
+  v::AbstractVector,
+  ghv::AbstractVector,
+)
+  increment!(nlp, :neval_hprod)
+  ghv .= 0.0
+  for i in nlp.meta.nlin + 1 : nlp.meta.nlin + nlp.quadcon.nquad
+    qcon = nlp.quadcon.constraints[i - nlp.meta.nlin]
+    ghv[i] = coo_sym_dot(qcon.A.rows, qcon.A.cols, qcon.A.vals, g, v)
+  end
+  for i in nlp.meta.nlin + nlp.quadcon.nquad + 1 : nlp.meta.ncon
+    jth_hprod!(nlp, x, v, i, nlp.hv)
+    decrement!(nlp, :neval_jhprod)
+    ghv[i] = dot(g, nlp.hv)
+  end
+  return ghv
+end
diff --git a/test/nlp_consistency.jl b/test/nlp_consistency.jl
index a2f034f..9f57b8e 100644
--- a/test/nlp_consistency.jl
+++ b/test/nlp_consistency.jl
@@ -4,7 +4,7 @@ for problem in nlp_problems
     problem_f = eval(Symbol(lowercase(problem)))
     nlp_moi = MathOptNLPModel(problem_f())
     nlps = [nlp_manual; nlp_moi]
-    consistent_nlps(nlps, linear_api = true, test_slack = false)
+    consistent_nlps(nlps, linear_api = true, test_slack = false, exclude = [])
     view_subarray_nlp(nlp_moi)
   end
 end