From 7273d2f59b79451f39f8fef390b85ca74c2bcd28 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 10 Mar 2022 10:37:03 -0500
Subject: [PATCH 01/16] [WIP] Quadratic constraints

---
 src/moi_nlp_model.jl |  28 +++++---
 src/moi_nls_model.jl |   2 +-
 src/utils.jl         | 155 ++++++++++++++++++++++++++++++++++++++++---
 3 files changed, 166 insertions(+), 19 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index 63e6745..05259e0 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -4,6 +4,9 @@ mutable struct MathOptNLPModel <: AbstractNLPModel{Float64, Vector{Float64}}
   meta::NLPModelMeta{Float64, Vector{Float64}}
   eval::Union{MOI.AbstractNLPEvaluator, Nothing}
   lincon::LinearConstraints
+  quadcon::Vector{QuadraticConstraint}
+  nquad::Int
+  nnln::Int
   obj::Objective
   counters::Counters
 end
@@ -33,7 +36,10 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     (nnln == 0 ? 0 : sum(length(nl_con.hess_I) for nl_con in eval.constraints)) : 0
 
   moimodel = backend(jmodel)
-  nlin, lincon, lin_lcon, lin_ucon = parser_MOI(moimodel)
+  nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
+  
+  
+  quad_nnzh = nquad == 0 ? 0 : sum(length(quadcon[i].vals) for i = 1 : nquad)
 
   if (eval ≠ nothing) && eval.has_nlobj
     obj = Objective("NONLINEAR", 0.0, spzeros(Float64, nvar), COO(), 0)
@@ -41,11 +47,11 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     obj = parser_objective_MOI(moimodel, nvar)
   end
 
-  ncon = nlin + nnln
-  lcon = vcat(lin_lcon, nl_lcon)
-  ucon = vcat(lin_ucon, nl_ucon)
-  nnzj = lincon.nnzj + nl_nnzj
-  nnzh = obj.nnzh + nl_nnzh
+  ncon = nlin + nquad + nnln
+  lcon = vcat(lin_lcon, quad_lcon, nl_lcon)
+  ucon = vcat(lin_ucon, quad_ucon, nl_ucon)
+  nnzj = lincon.nnzj + ... + nl_nnzj
+  nnzh = obj.nnzh + quad_nnzh + nl_nnzh
 
   meta = NLPModelMeta(
     nvar,
@@ -62,11 +68,11 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     lin_nnzj = lincon.nnzj,
     nln_nnzj = nl_nnzj,
     minimize = objective_sense(jmodel) == MOI.MIN_SENSE,
-    islp = (obj.type == "LINEAR") && (nnln == 0),
+    islp = (obj.type == "LINEAR") && (nnln == 0) && (nquad == 0),
     name = name,
   )
 
-  return MathOptNLPModel(meta, eval, lincon, obj, Counters())
+  return MathOptNLPModel(meta, eval, lincon, quadcon, nquad, obj, Counters())
 end
 
 function NLPModels.obj(nlp::MathOptNLPModel, x::AbstractVector)
@@ -115,7 +121,11 @@ end
 
 function NLPModels.cons_nln!(nlp::MathOptNLPModel, x::AbstractVector, c::AbstractVector)
   increment!(nlp, :neval_cons_nln)
-  MOI.eval_constraint(nlp.eval, c, x)
+  for i = 1 : nlp.nquad
+    qcon = nlp.quadcon[i]
+    c[i] = 0.5 * coo_sym_dot(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, x, x) + dot(qcon.b, x)
+  end
+  MOI.eval_constraint(nlp.eval, view(c, (nlp.nquad + 1):(nlp.meta.nnln)), x)
   return c
 end
 
diff --git a/src/moi_nls_model.jl b/src/moi_nls_model.jl
index 29bf10b..cb74649 100644
--- a/src/moi_nls_model.jl
+++ b/src/moi_nls_model.jl
@@ -40,7 +40,7 @@ function MathOptNLSModel(cmodel::JuMP.Model, F; hessian::Bool = true, name::Stri
     (nnln == 0 ? 0 : sum(length(con.hess_I) for con in ceval.constraints)) : 0
 
   moimodel = backend(cmodel)
-  nlin, lincon, lin_lcon, lin_ucon = parser_MOI(moimodel)
+  nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
 
   nequ = nlinequ + nnlnequ
   Fnnzj = linequ.nnzj + nl_Fnnzj
diff --git a/src/utils.jl b/src/utils.jl
index 5910610..f2671c4 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -6,10 +6,18 @@ import NLPModels.increment!, NLPModels.decrement!
 using JuMP, MathOptInterface
 const MOI = MathOptInterface
 
+# VariableIndex
+const VI = MOI.VariableIndex  # VariableIndex(value)
+
 # ScalarAffineFunctions and VectorAffineFunctions
-const SAF = MOI.ScalarAffineFunction{Float64}
-const VAF = MOI.VectorAffineFunction{Float64}
-const AF = Union{SAF, VAF}
+const SAF = MOI.ScalarAffineFunction{Float64}  # ScalarAffineFunction{T}(terms, constant)
+const VAF = MOI.VectorAffineFunction{Float64}  # VectorAffineFunction{T}(terms, constants)
+const AF  = Union{SAF, VAF}
+
+# ScalarQuadraticFunctions and VectorQuadraticFunctions
+const SQF = MOI.ScalarQuadraticFunction{Float64}  # ScalarQuadraticFunction{T}(affine_terms, quadratic_terms, constant)
+const VQF = MOI.VectorQuadraticFunction{Float64}  # VectorQuadraticFunction{T}(affine_terms, quadratic_terms, constants)
+const QF  = Union{SQF, VQF}
 
 # AffLinSets and VecLinSets
 const ALS = Union{
@@ -21,10 +29,11 @@ const ALS = Union{
 const VLS = Union{MOI.Nonnegatives, MOI.Nonpositives, MOI.Zeros}
 const LS = Union{ALS, VLS}
 
+# Objective
 const VI = MOI.VariableIndex
-const SQF = MOI.ScalarQuadraticFunction{Float64}
 const OBJ = Union{VI, SAF, SQF}
 
+# Coordinate Matrix
 mutable struct COO
   rows::Vector{Int}
   cols::Vector{Int}
@@ -38,6 +47,21 @@ mutable struct LinearConstraints
   nnzj::Int
 end
 
+mutable struct QuadraticConstraint
+  hessian::COO
+  b::SparseVector{Float64}
+end
+
+mutable struct QuadraticConstraints
+  qcons::Vector{QuadraticConstraint}
+  nnzj::Int
+  jrows::Vector{Int}
+  jcols::Vector{Int}
+  nnzh::Int
+  hrows::Vector{Int}
+  hcols::Vector{Int}
+end
+
 mutable struct LinearEquations
   jacobian::COO
   constants::Vector{Float64}
@@ -96,6 +120,52 @@ function coo_sym_dot(
   return xᵀAy
 end
 
+"""
+    jacobian_quad(qcons)
+
+`qcons` is a vector of `QuadraticConstraint` where each constraint has the form ½xᵀQᵢx + xᵀbᵢ.
+Compute the sparcity pattern of the jacobian [Q₁x + b₁; ...; Qₚx + bₚ]ᵀ of `qcons`.
+"""
+function jacobian_quad(qcons)
+  jrows = Int[]
+  jcols = Int[]
+  nquad = length(qcons)
+  for i = 1 : nquad
+    # rows of Qᵢx + bᵢ with nonzeros coefficients
+    vec = unique(con.hessian.rows ∪ con.b.nzind)
+    for elt ∈ vec
+      push!(elt, jcols)
+      push!(i, jrows)
+    end
+  end
+  nnzj = length(jrows)
+  return nnzj, jrows, jcols
+end
+
+"""
+    hessian_quad(qcons)
+
+`qcons` is a vector of `QuadraticConstraint` where each constraint has the form ½xᵀQᵢx + xᵀbᵢ.
+Compute the sparcity pattern of the hessian ΣᵢQᵢ of `qcons`.
+"""
+function hessian_quad(qcons)
+  set = Set{Tuple{Int,Int}}()
+  for con ∈ qcons
+    for tuple ∈ zip(con.rows, con.vals)
+      # Only disctinct tuples are stored in the set
+      push!(tuple, set)
+    end
+  end
+  nnzh = length(set)
+  hrows = zeros(Int, nnzh)
+  hcols = zeros(Int, nnzh)
+  for (index,tuple) in enumerate(set)
+    hrows[index] = tuple[1]
+    hcols[index] = tuple[2]
+  end
+  return nnzh, hrows, hcols
+end
+
 """
     parser_SAF(fun, set, linrows, lincols, linvals, nlin, lin_lcon, lin_ucon)
 
@@ -157,11 +227,64 @@ function parser_VAF(fun, set, linrows, lincols, linvals, nlin, lin_lcon, lin_uco
 end
 
 """
-    parser_MOI(moimodel)
+    parser_SQF(fun, set, qcons, quad_lcon, quad_ucon)
 
-Parse linear constraints of a `MOI.ModelLike`.
+Parse a `ScalarQuadraticFunction` fun with its associated set.
+`qcons`, `quad_lcon`, `quad_ucon` are updated.
 """
-function parser_MOI(moimodel)
+function parser_SQF(fun, set, nvar, qcons, quad_lcon, quad_ucon)
+
+  b    = spzeros(Float64, nvar)
+  rows = Int[]
+  cols = Int[]
+  vals = Float64[]
+
+  # Parse a ScalarAffineTerm{Float64}(coefficient, variable_index)
+  for term in fun.affine_terms
+    b[term.variable.value] = term.coefficient
+  end
+
+  # Parse a ScalarQuadraticTerm{Float64}(coefficient, variable_index_1, variable_index_2)
+  for term in fun.quadratic_terms
+    i = term.variable_1.value
+    j = term.variable_2.value
+    if i ≥ j
+      push!(rows, i)
+      push!(cols, j)
+    else
+      push!(cols, j)
+      push!(rows, i)
+    end
+    push!(vals, term.coefficient)
+  end
+
+  if typeof(set) in (MOI.Interval{Float64}, MOI.GreaterThan{Float64})
+    push!(quad_lcon, -fun.constant + set.lower)
+  elseif typeof(set) == MOI.EqualTo{Float64}
+    push!(quad_lcon, -fun.constant + set.value)
+  else
+    push!(quad_lcon, -Inf)
+  end
+
+  if typeof(set) in (MOI.Interval{Float64}, MOI.LessThan{Float64})
+    push!(quad_ucon, -fun.constant + set.upper)
+  elseif typeof(set) == MOI.EqualTo{Float64}
+    push!(quad_ucon, -fun.constant + set.value)
+  else
+    push!(quad_ucon, Inf)
+  end
+
+  nnzh = length(vals)
+  qcon = QuadraticConstraint(COO[rows, cols, vals], b)
+  push!(qcons, qcon)
+end
+
+"""
+    parser_MOI(moimodel, nvar)
+
+Parse linear and quadratic constraints of a `MOI.ModelLike`.
+"""
+function parser_MOI(moimodel, nvar)
 
   # Variables associated to linear constraints
   nlin = 0
@@ -171,10 +294,16 @@ function parser_MOI(moimodel)
   lin_lcon = Float64[]
   lin_ucon = Float64[]
 
+  # Variables associated to quadratic constraints
+  nquad = 0
+  qcons = QuadraticConstraint[]
+  quad_lcon = Float64[]
+  quad_ucon = Float64[]
+
   contypes = MOI.get(moimodel, MOI.ListOfConstraintTypesPresent())
   for (F, S) in contypes
     F == VI && continue
-    F <: AF || @warn("Function $F is not supported.")
+    F <: AF || F <: SQF || @warn("Function $F is not supported.")
     S <: LS || @warn("Set $S is not supported.")
 
     conindices = MOI.get(moimodel, MOI.ListOfConstraintIndices{F, S}())
@@ -189,13 +318,21 @@ function parser_MOI(moimodel)
         parser_VAF(fun, set, linrows, lincols, linvals, nlin, lin_lcon, lin_ucon)
         nlin += set.dimension
       end
+      if typeof(fun) <: SQF
+        parser_SQF(fun, set, nvar, qcons, quad_lcon, quad_ucon)
+        nquad += 1
+      end
     end
   end
   coo = COO(linrows, lincols, linvals)
   nnzj = length(linvals)
   lincon = LinearConstraints(coo, nnzj)
 
-  return nlin, lincon, lin_lcon, lin_ucon
+  nnzj, jrows, jcols = jacobian_quad(qcons)
+  nnzh, hrows, hcols = hessian_quad(qcons)
+  quadcon = QuadraticConstraints(qcons, nnzj, jrows, jcols, nnzh, hrows, hcols)
+
+  return nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon
 end
 
 """

From 69903087cedc970bca79499d2be7dfeb734132ba Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Fri, 6 May 2022 14:59:44 -0400
Subject: [PATCH 02/16] add straightforward test

---
 test/nlp_problems/hs61.jl  | 12 ++++++++++++
 test/runtests.jl           |  2 +-
 test/test_moi_nlp_model.jl |  2 +-
 3 files changed, 14 insertions(+), 2 deletions(-)
 create mode 100644 test/nlp_problems/hs61.jl

diff --git a/test/nlp_problems/hs61.jl b/test/nlp_problems/hs61.jl
new file mode 100644
index 0000000..5e422cc
--- /dev/null
+++ b/test/nlp_problems/hs61.jl
@@ -0,0 +1,12 @@
+"HS61 model"
+function hs61(args...; kwargs...)
+  nlp = Model()
+  @variable(nlp, x[i = 1:3], start = 0)
+
+  @constraint(nlp, 3 * x[1] - 2 * x[2]^2 - 7 == 0)
+  @constraint(nlp, 4 * x[1] - x[3]^2 - 11 == 0)
+
+  @NLobjective(nlp, Min, 4 * x[1]^2 + 2 * x[2]^2 + 2 * x[3]^2 - 33 * x[1] + 16 * x[2] - 24 * x[3])
+
+  return nlp
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 5306ee7..13fa408 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -6,7 +6,7 @@ nlp_problems = setdiff(NLPModelsTest.nlp_problems, ["MGH01Feas"])
 nls_problems = NLPModelsTest.nls_problems
 extra_nls_problems = ["HS30", "HS43", "MGH07", "nlsnohesspb"]
 
-for problem in lowercase.(nlp_problems ∪ ["nohesspb"])
+for problem in lowercase.(nlp_problems ∪ ["nohesspb", "hs61"])
   include(joinpath("nlp_problems", "$problem.jl"))
 end
 
diff --git a/test/test_moi_nlp_model.jl b/test/test_moi_nlp_model.jl
index 162694d..dd2dfb5 100644
--- a/test/test_moi_nlp_model.jl
+++ b/test/test_moi_nlp_model.jl
@@ -11,7 +11,7 @@ println("Testing MathOptNLPModel")
   "‖c(x₀)‖"
 )
 # Test that every problem can be instantiated.
-for prob in Symbol.(lowercase.(nlp_problems ∪ ["nohesspb"]))
+for prob in Symbol.(lowercase.(nlp_problems ∪ ["nohesspb", "hs61"]))
   prob_fn = eval(prob)
   nlp = MathOptNLPModel(prob_fn(), hessian = (prob != :nohesspb))
   n = nlp.meta.nvar

From 2b1574d9b1ab2e956cb99e45322c8e57a60c9fad Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Fri, 6 May 2022 15:01:50 -0400
Subject: [PATCH 03/16] debug utils functions

---
 src/utils.jl | 26 ++++++++++++++++----------
 1 file changed, 16 insertions(+), 10 deletions(-)

diff --git a/src/utils.jl b/src/utils.jl
index f2671c4..710bed8 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -54,6 +54,7 @@ end
 
 mutable struct QuadraticConstraints
   qcons::Vector{QuadraticConstraint}
+  nquad::Int
   nnzj::Int
   jrows::Vector{Int}
   jcols::Vector{Int}
@@ -62,6 +63,9 @@ mutable struct QuadraticConstraints
   hcols::Vector{Int}
 end
 
+Base.getindex(qcon::QuadraticConstraints, i::Integer) = qcon.qcons[i]
+Base.length(qcon::QuadraticConstraints) = qcon.nquad
+
 mutable struct LinearEquations
   jacobian::COO
   constants::Vector{Float64}
@@ -124,7 +128,7 @@ end
     jacobian_quad(qcons)
 
 `qcons` is a vector of `QuadraticConstraint` where each constraint has the form ½xᵀQᵢx + xᵀbᵢ.
-Compute the sparcity pattern of the jacobian [Q₁x + b₁; ...; Qₚx + bₚ]ᵀ of `qcons`.
+Compute the sparsity pattern of the jacobian [Q₁x + b₁; ...; Qₚx + bₚ]ᵀ of `qcons`.
 """
 function jacobian_quad(qcons)
   jrows = Int[]
@@ -132,10 +136,10 @@ function jacobian_quad(qcons)
   nquad = length(qcons)
   for i = 1 : nquad
     # rows of Qᵢx + bᵢ with nonzeros coefficients
-    vec = unique(con.hessian.rows ∪ con.b.nzind)
+    vec = unique(qcons[i].hessian.rows ∪ qcons[i].b.nzind)
     for elt ∈ vec
-      push!(elt, jcols)
-      push!(i, jrows)
+      push!(jcols, elt)
+      push!(jrows, i)
     end
   end
   nnzj = length(jrows)
@@ -146,14 +150,16 @@ end
     hessian_quad(qcons)
 
 `qcons` is a vector of `QuadraticConstraint` where each constraint has the form ½xᵀQᵢx + xᵀbᵢ.
-Compute the sparcity pattern of the hessian ΣᵢQᵢ of `qcons`.
+Compute the sparsity pattern of the hessian ΣᵢQᵢ of `qcons`.
 """
 function hessian_quad(qcons)
   set = Set{Tuple{Int,Int}}()
-  for con ∈ qcons
-    for tuple ∈ zip(con.rows, con.vals)
+  nquad = length(qcons)
+  for i = 1 : nquad
+    con = qcons[i]
+    for tuple ∈ zip(con.hessian.rows, con.hessian.cols)
       # Only disctinct tuples are stored in the set
-      push!(tuple, set)
+      push!(set, tuple)
     end
   end
   nnzh = length(set)
@@ -275,7 +281,7 @@ function parser_SQF(fun, set, nvar, qcons, quad_lcon, quad_ucon)
   end
 
   nnzh = length(vals)
-  qcon = QuadraticConstraint(COO[rows, cols, vals], b)
+  qcon = QuadraticConstraint(COO(rows, cols, vals), b)
   push!(qcons, qcon)
 end
 
@@ -330,7 +336,7 @@ function parser_MOI(moimodel, nvar)
 
   nnzj, jrows, jcols = jacobian_quad(qcons)
   nnzh, hrows, hcols = hessian_quad(qcons)
-  quadcon = QuadraticConstraints(qcons, nnzj, jrows, jcols, nnzh, hrows, hcols)
+  quadcon = QuadraticConstraints(qcons, nquad, nnzj, jrows, jcols, nnzh, hrows, hcols)
 
   return nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon
 end

From 3bec27bbf12d81a53c30a49be642e362b4478cf4 Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Fri, 6 May 2022 15:02:18 -0400
Subject: [PATCH 04/16] add API for quadratic constraints

---
 src/moi_nlp_model.jl | 71 +++++++++++++++++++++++++++++++-------------
 1 file changed, 50 insertions(+), 21 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index 05259e0..5c61341 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -4,9 +4,7 @@ mutable struct MathOptNLPModel <: AbstractNLPModel{Float64, Vector{Float64}}
   meta::NLPModelMeta{Float64, Vector{Float64}}
   eval::Union{MOI.AbstractNLPEvaluator, Nothing}
   lincon::LinearConstraints
-  quadcon::Vector{QuadraticConstraint}
-  nquad::Int
-  nnln::Int
+  quadcon::QuadraticConstraints
   obj::Objective
   counters::Counters
 end
@@ -37,9 +35,6 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
 
   moimodel = backend(jmodel)
   nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
-  
-  
-  quad_nnzh = nquad == 0 ? 0 : sum(length(quadcon[i].vals) for i = 1 : nquad)
 
   if (eval ≠ nothing) && eval.has_nlobj
     obj = Objective("NONLINEAR", 0.0, spzeros(Float64, nvar), COO(), 0)
@@ -50,8 +45,8 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
   ncon = nlin + nquad + nnln
   lcon = vcat(lin_lcon, quad_lcon, nl_lcon)
   ucon = vcat(lin_ucon, quad_ucon, nl_ucon)
-  nnzj = lincon.nnzj + ... + nl_nnzj
-  nnzh = obj.nnzh + quad_nnzh + nl_nnzh
+  nnzj = lincon.nnzj + quadcon.nnzj + nl_nnzj
+  nnzh = obj.nnzh + quadcon.nnzh + nl_nnzh
 
   meta = NLPModelMeta(
     nvar,
@@ -66,13 +61,13 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     nnzh = nnzh,
     lin = collect(1:nlin),
     lin_nnzj = lincon.nnzj,
-    nln_nnzj = nl_nnzj,
+    nln_nnzj = quadcon.nnzj + nl_nnzj,
     minimize = objective_sense(jmodel) == MOI.MIN_SENSE,
     islp = (obj.type == "LINEAR") && (nnln == 0) && (nquad == 0),
     name = name,
   )
 
-  return MathOptNLPModel(meta, eval, lincon, quadcon, nquad, obj, Counters())
+  return MathOptNLPModel(meta, eval, lincon, quadcon, obj, Counters())
 end
 
 function NLPModels.obj(nlp::MathOptNLPModel, x::AbstractVector)
@@ -121,11 +116,11 @@ end
 
 function NLPModels.cons_nln!(nlp::MathOptNLPModel, x::AbstractVector, c::AbstractVector)
   increment!(nlp, :neval_cons_nln)
-  for i = 1 : nlp.nquad
+  for i = 1:(nlp.quadcon.nquad)
     qcon = nlp.quadcon[i]
     c[i] = 0.5 * coo_sym_dot(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, x, x) + dot(qcon.b, x)
   end
-  MOI.eval_constraint(nlp.eval, view(c, (nlp.nquad + 1):(nlp.meta.nnln)), x)
+  MOI.eval_constraint(nlp.eval, view(c, (nlp.quadcon.nquad + 1):(nlp.meta.nnln)), x)
   return c
 end
 
@@ -144,10 +139,13 @@ function NLPModels.jac_nln_structure!(
   rows::AbstractVector{<:Integer},
   cols::AbstractVector{<:Integer},
 )
+  quad_nnzj, jrows, jcols = nlp.quadcon.nnzj, nlp.quadcon.jrows, nlp.quadcon.jcols
+  rows[1:quad_nnzj] .= jrows
+  cols[1:quad_nnzj] .= jcols
   jac_struct = MOI.jacobian_structure(nlp.eval)
-  for index = 1:(nlp.meta.nln_nnzj)
+  for index = (quad_nnzj + 1):(nlp.meta.nln_nnzj)
     row, col = jac_struct[index]
-    rows[index] = row
+    rows[index] = row + nlp.quadcon.nquad
     cols[index] = col
   end
   return rows, cols
@@ -161,7 +159,19 @@ end
 
 function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals::AbstractVector)
   increment!(nlp, :neval_jac_nln)
-  MOI.eval_constraint_jacobian(nlp.eval, vals, x)
+  quad_nnzj = nlp.quadcon.nnzj
+  k = 0
+  for i = 1:(nlp.quadcon.nquad)
+    # rows of Qᵢx + bᵢ with nonzeros coefficients
+    qcon = nlp.quadcon[i]
+    vec = unique(qcon.hessian.rows ∪ qcon.b.nzind) # Can we improve here? Or store this information?
+    nnzj = length(vec)
+    res = similar(x) # Avoid extra allocation
+    coo_sym_prod!(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, x, res)
+    vals[(k + 1):(k + nnzj)] .= res[vec] .+ qcon.b[vec]
+    k += nnzj
+  end
+  MOI.eval_constraint_jacobian(nlp.eval, view(vals, (quad_nnzj + 1):(nlp.meta.nln_nnzj)), x)
   return vals
 end
 
@@ -316,9 +326,12 @@ function NLPModels.hess_structure!(
     end
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
+    quad_nnzh = nlp.quadcon.nnzh
+    rows[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= nlp.quadcon.hrows
+    cols[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= nlp.quadcon.hcols
     hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)
-    for index = (nlp.obj.nnzh + 1):(nlp.meta.nnzh)
-      shift_index = index - nlp.obj.nnzh
+    for index = (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)
+      shift_index = index - nlp.obj.nnzh - quad_nnzh
       rows[index] = hesslag_struct[shift_index][1]
       cols[index] = hesslag_struct[shift_index][2]
     end
@@ -338,12 +351,20 @@ function NLPModels.hess_coord!(
     vals[1:(nlp.obj.nnzh)] .= obj_weight .* nlp.obj.hessian.vals
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
+    quad_nnzh = nlp.quadcon.nnzh
+    k = 0
+    for i = 1:(nlp.quadcon.nquad)
+      qcon = nlp.quadcon[i]
+      nnzh = length(qcon.hessian.vals)
+      vals[(k + 1):(k + nnzh)] .= qcon.hessian.vals .* y[nlp.meta.nlin + i]
+      k += nnzh
+    end
     MOI.eval_hessian_lagrangian(
       nlp.eval,
-      view(vals, (nlp.obj.nnzh + 1):(nlp.meta.nnzh)),
+      view(vals, (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)),
       x,
       obj_weight,
-      view(y, nlp.meta.nln),
+      view(y, (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)),
     )
   end
   return vals
@@ -383,7 +404,14 @@ function NLPModels.hprod!(
     hv .= 0.0
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
-    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, nlp.meta.nln))
+    for i = 1:(nlp.quadcon.nquad)
+      qcon = nlp.quadcon[i]
+      res = similar(x) # Avoid extra allocation
+      coo_sym_prod!(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, v, res)
+      hv .+= res .* y[nlp.meta.nlin + i]
+    end
+    ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)
+    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
   end
   if nlp.obj.type == "QUADRATIC"
     nlp.meta.nnln == 0 && (hv .= 0.0)
@@ -414,7 +442,8 @@ function NLPModels.hprod!(
     hv .*= obj_weight
   end
   if nlp.obj.type == "NONLINEAR"
-    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, zeros(nlp.meta.nnln))
+    nnln = nlp.meta.nnln - nlp.quadcon.nquad
+    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, zeros(nnln))
   end
   return hv
 end

From 0f08e9aaca140a030aec685ff9f311f025d7bea5 Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Fri, 6 May 2022 15:35:04 -0400
Subject: [PATCH 05/16] simplify `nquad`

---
 src/moi_nlp_model.jl | 6 +++---
 src/moi_nls_model.jl | 2 +-
 src/utils.jl         | 2 +-
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index 5c61341..c208e9d 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -34,7 +34,7 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     (nnln == 0 ? 0 : sum(length(nl_con.hess_I) for nl_con in eval.constraints)) : 0
 
   moimodel = backend(jmodel)
-  nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
+  nlin, lincon, lin_lcon, lin_ucon, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
 
   if (eval ≠ nothing) && eval.has_nlobj
     obj = Objective("NONLINEAR", 0.0, spzeros(Float64, nvar), COO(), 0)
@@ -42,7 +42,7 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     obj = parser_objective_MOI(moimodel, nvar)
   end
 
-  ncon = nlin + nquad + nnln
+  ncon = nlin + quadcon.nquad + nnln
   lcon = vcat(lin_lcon, quad_lcon, nl_lcon)
   ucon = vcat(lin_ucon, quad_ucon, nl_ucon)
   nnzj = lincon.nnzj + quadcon.nnzj + nl_nnzj
@@ -63,7 +63,7 @@ function MathOptNLPModel(jmodel::JuMP.Model; hessian::Bool = true, name::String
     lin_nnzj = lincon.nnzj,
     nln_nnzj = quadcon.nnzj + nl_nnzj,
     minimize = objective_sense(jmodel) == MOI.MIN_SENSE,
-    islp = (obj.type == "LINEAR") && (nnln == 0) && (nquad == 0),
+    islp = (obj.type == "LINEAR") && (nnln == 0) && (quadcon.nquad == 0),
     name = name,
   )
 
diff --git a/src/moi_nls_model.jl b/src/moi_nls_model.jl
index cb74649..01f1160 100644
--- a/src/moi_nls_model.jl
+++ b/src/moi_nls_model.jl
@@ -40,7 +40,7 @@ function MathOptNLSModel(cmodel::JuMP.Model, F; hessian::Bool = true, name::Stri
     (nnln == 0 ? 0 : sum(length(con.hess_I) for con in ceval.constraints)) : 0
 
   moimodel = backend(cmodel)
-  nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
+  nlin, lincon, lin_lcon, lin_ucon, quadcon, quad_lcon, quad_ucon = parser_MOI(moimodel, nvar)
 
   nequ = nlinequ + nnlnequ
   Fnnzj = linequ.nnzj + nl_Fnnzj
diff --git a/src/utils.jl b/src/utils.jl
index 710bed8..4ce5e60 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -338,7 +338,7 @@ function parser_MOI(moimodel, nvar)
   nnzh, hrows, hcols = hessian_quad(qcons)
   quadcon = QuadraticConstraints(qcons, nquad, nnzj, jrows, jcols, nnzh, hrows, hcols)
 
-  return nlin, lincon, lin_lcon, lin_ucon, nquad, quadcon, quad_lcon, quad_ucon
+  return nlin, lincon, lin_lcon, lin_ucon, quadcon, quad_lcon, quad_ucon
 end
 
 """

From af04c2ee82d0582a1a1efa5adc9179fb7fa68feb Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Wed, 11 May 2022 00:03:06 +0200
Subject: [PATCH 06/16] add hs100

---
 test/nlp_problems/hs100.jl | 24 ++++++++++++++++++++++++
 test/runtests.jl           |  2 +-
 test/test_moi_nlp_model.jl |  2 +-
 3 files changed, 26 insertions(+), 2 deletions(-)
 create mode 100644 test/nlp_problems/hs100.jl

diff --git a/test/nlp_problems/hs100.jl b/test/nlp_problems/hs100.jl
new file mode 100644
index 0000000..2dca312
--- /dev/null
+++ b/test/nlp_problems/hs100.jl
@@ -0,0 +1,24 @@
+function hs100(args...; kwargs...)
+  nlp = Model()
+  x0 = [1, 2, 0, 4, 0, 1, 1]
+  @variable(nlp, x[i = 1:7], start = x0[i])
+
+  @NLconstraint(nlp, 127 - 2 * x[1]^2 - 3 * x[2]^4 - x[3] - 4 * x[4]^2 - 5 * x[5] ≥ 0)
+  @constraint(nlp, 282 - 7 * x[1] - 3 * x[2] - 10 * x[3]^2 - x[4] + x[5] ≥ 0)
+  @constraint(nlp, 196 - 23 * x[1] - x[2]^2 - 6 * x[6]^2 + 8 * x[7] ≥ 0)
+  @constraint(nlp, -4 * x[1]^2 - x[2]^2 + 3 * x[1] * x[2] - 2 * x[3]^2 - 5 * x[6] + 11 * x[7] ≥ 0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    (x[1] - 10)^2 +
+    5 * (x[2] - 12)^2 +
+    x[3]^4 +
+    3 * (x[4] - 11)^2 +
+    10 * x[5]^6 +
+    7 * x[6]^2 +
+    x[7]^4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]
+  )
+
+  return nlp
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 13fa408..7a34589 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -6,7 +6,7 @@ nlp_problems = setdiff(NLPModelsTest.nlp_problems, ["MGH01Feas"])
 nls_problems = NLPModelsTest.nls_problems
 extra_nls_problems = ["HS30", "HS43", "MGH07", "nlsnohesspb"]
 
-for problem in lowercase.(nlp_problems ∪ ["nohesspb", "hs61"])
+for problem in lowercase.(nlp_problems ∪ ["nohesspb", "hs61", "hs100"])
   include(joinpath("nlp_problems", "$problem.jl"))
 end
 
diff --git a/test/test_moi_nlp_model.jl b/test/test_moi_nlp_model.jl
index dd2dfb5..4f236ba 100644
--- a/test/test_moi_nlp_model.jl
+++ b/test/test_moi_nlp_model.jl
@@ -11,7 +11,7 @@ println("Testing MathOptNLPModel")
   "‖c(x₀)‖"
 )
 # Test that every problem can be instantiated.
-for prob in Symbol.(lowercase.(nlp_problems ∪ ["nohesspb", "hs61"]))
+for prob in Symbol.(lowercase.(nlp_problems ∪ ["nohesspb", "hs61", "hs100"]))
   prob_fn = eval(prob)
   nlp = MathOptNLPModel(prob_fn(), hessian = (prob != :nohesspb))
   n = nlp.meta.nvar

From 2aaf3539f422a828134f8be0c922c563351eac1f Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Wed, 11 May 2022 00:21:41 +0200
Subject: [PATCH 07/16] store `vec`

---
 src/moi_nlp_model.jl | 2 +-
 src/utils.jl         | 8 +++++---
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index c208e9d..863626f 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -164,7 +164,7 @@ function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals:
   for i = 1:(nlp.quadcon.nquad)
     # rows of Qᵢx + bᵢ with nonzeros coefficients
     qcon = nlp.quadcon[i]
-    vec = unique(qcon.hessian.rows ∪ qcon.b.nzind) # Can we improve here? Or store this information?
+    vec = nlp.quadcon[i].vec # unique(qcon.hessian.rows ∪ qcon.b.nzind) # Can we improve here? Or store this information?
     nnzj = length(vec)
     res = similar(x) # Avoid extra allocation
     coo_sym_prod!(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, x, res)
diff --git a/src/utils.jl b/src/utils.jl
index 4ce5e60..0abca16 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -49,6 +49,7 @@ end
 
 mutable struct QuadraticConstraint
   hessian::COO
+  vec::Vector{Int}
   b::SparseVector{Float64}
 end
 
@@ -129,6 +130,7 @@ end
 
 `qcons` is a vector of `QuadraticConstraint` where each constraint has the form ½xᵀQᵢx + xᵀbᵢ.
 Compute the sparsity pattern of the jacobian [Q₁x + b₁; ...; Qₚx + bₚ]ᵀ of `qcons`.
+This function also allocates `qcons[i].vec`.
 """
 function jacobian_quad(qcons)
   jrows = Int[]
@@ -136,8 +138,8 @@ function jacobian_quad(qcons)
   nquad = length(qcons)
   for i = 1 : nquad
     # rows of Qᵢx + bᵢ with nonzeros coefficients
-    vec = unique(qcons[i].hessian.rows ∪ qcons[i].b.nzind)
-    for elt ∈ vec
+    qcons[i].vec = unique(qcons[i].hessian.rows ∪ qcons[i].b.nzind)
+    for elt ∈ qcons[i].vec
       push!(jcols, elt)
       push!(jrows, i)
     end
@@ -281,7 +283,7 @@ function parser_SQF(fun, set, nvar, qcons, quad_lcon, quad_ucon)
   end
 
   nnzh = length(vals)
-  qcon = QuadraticConstraint(COO(rows, cols, vals), b)
+  qcon = QuadraticConstraint(COO(rows, cols, vals), Int[], b)
   push!(qcons, qcon)
 end
 

From 90ea72a79a38d83ce667d4210f5f937bdc7cd736 Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Wed, 11 May 2022 01:14:45 +0200
Subject: [PATCH 08/16] implement hprod and jac_coord properly

---
 src/moi_nlp_model.jl | 28 ++++++++++++++++------------
 src/utils.jl         | 14 +++++++++-----
 2 files changed, 25 insertions(+), 17 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index 863626f..e62f052 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -157,18 +157,20 @@ function NLPModels.jac_lin_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals:
   return vals
 end
 
-function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals::AbstractVector)
+function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals::AbstractVector{T}) where {T}
   increment!(nlp, :neval_jac_nln)
   quad_nnzj = nlp.quadcon.nnzj
   k = 0
   for i = 1:(nlp.quadcon.nquad)
-    # rows of Qᵢx + bᵢ with nonzeros coefficients
     qcon = nlp.quadcon[i]
-    vec = nlp.quadcon[i].vec # unique(qcon.hessian.rows ∪ qcon.b.nzind) # Can we improve here? Or store this information?
-    nnzj = length(vec)
-    res = similar(x) # Avoid extra allocation
-    coo_sym_prod!(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, x, res)
-    vals[(k + 1):(k + nnzj)] .= res[vec] .+ qcon.b[vec]
+    vec = qcon.vec
+    for j=1:length(vec)
+      vals[k + j] = qcon.b[j]
+    end
+    nnzj = length(qcon.hessian.vals)
+    for i=1:nnzj
+      vals[k + qcon.hessian.rows[i]] += qcon.hessian.vals[i] * x[qcon.hessian.cols[i]]
+    end
     k += nnzj
   end
   MOI.eval_constraint_jacobian(nlp.eval, view(vals, (quad_nnzj + 1):(nlp.meta.nln_nnzj)), x)
@@ -327,8 +329,9 @@ function NLPModels.hess_structure!(
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
     quad_nnzh = nlp.quadcon.nnzh
-    rows[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= nlp.quadcon.hrows
-    cols[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= nlp.quadcon.hcols
+    hrows, hcols = hessian_structure(nlp.quadcon.set)
+    rows[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= hrows
+    cols[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= hcols
     hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)
     for index = (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)
       shift_index = index - nlp.obj.nnzh - quad_nnzh
@@ -406,9 +409,10 @@ function NLPModels.hprod!(
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
     for i = 1:(nlp.quadcon.nquad)
       qcon = nlp.quadcon[i]
-      res = similar(x) # Avoid extra allocation
-      coo_sym_prod!(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, v, res)
-      hv .+= res .* y[nlp.meta.nlin + i]
+      for (index,tuple) in enumerate(nlp.quadcon.set)
+        hv[tuple[1]] += qcon.hessian.vals[index] * v[tuple[2]]
+      end
+      hv .*= y[nlp.meta.nlin + i]
     end
     ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)
     MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
diff --git a/src/utils.jl b/src/utils.jl
index 0abca16..bfa0842 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -60,8 +60,7 @@ mutable struct QuadraticConstraints
   jrows::Vector{Int}
   jcols::Vector{Int}
   nnzh::Int
-  hrows::Vector{Int}
-  hcols::Vector{Int}
+  set::Set{Tuple{Int,Int}}
 end
 
 Base.getindex(qcon::QuadraticConstraints, i::Integer) = qcon.qcons[i]
@@ -164,6 +163,10 @@ function hessian_quad(qcons)
       push!(set, tuple)
     end
   end
+  return set
+end
+
+function hessian_structure(set)
   nnzh = length(set)
   hrows = zeros(Int, nnzh)
   hcols = zeros(Int, nnzh)
@@ -171,7 +174,7 @@ function hessian_quad(qcons)
     hrows[index] = tuple[1]
     hcols[index] = tuple[2]
   end
-  return nnzh, hrows, hcols
+  return hrows, hcols
 end
 
 """
@@ -337,8 +340,9 @@ function parser_MOI(moimodel, nvar)
   lincon = LinearConstraints(coo, nnzj)
 
   nnzj, jrows, jcols = jacobian_quad(qcons)
-  nnzh, hrows, hcols = hessian_quad(qcons)
-  quadcon = QuadraticConstraints(qcons, nquad, nnzj, jrows, jcols, nnzh, hrows, hcols)
+  set = hessian_quad(qcons)
+  nnzh = length(set)
+  quadcon = QuadraticConstraints(qcons, nquad, nnzj, jrows, jcols, nnzh, set)
 
   return nlin, lincon, lin_lcon, lin_ucon, quadcon, quad_lcon, quad_ucon
 end

From 836a7b955ba74d88723e79ad3a1149a8dfdffdaf Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Wed, 11 May 2022 05:01:59 +0200
Subject: [PATCH 09/16] add test problem and fix

---
 src/moi_nlp_model.jl       | 21 +++++++++---------
 test/test_moi_nlp_model.jl | 44 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 55 insertions(+), 10 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index e62f052..fa9b782 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -143,10 +143,10 @@ function NLPModels.jac_nln_structure!(
   rows[1:quad_nnzj] .= jrows
   cols[1:quad_nnzj] .= jcols
   jac_struct = MOI.jacobian_structure(nlp.eval)
-  for index = (quad_nnzj + 1):(nlp.meta.nln_nnzj)
+  for index =  1:(nlp.meta.nln_nnzj - quad_nnzj)
     row, col = jac_struct[index]
-    rows[index] = row + nlp.quadcon.nquad
-    cols[index] = col
+    rows[quad_nnzj + index] = row + nlp.quadcon.nquad
+    cols[quad_nnzj + index] = col
   end
   return rows, cols
 end
@@ -157,19 +157,19 @@ function NLPModels.jac_lin_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals:
   return vals
 end
 
-function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals::AbstractVector{T}) where {T}
+function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals::AbstractVector)
   increment!(nlp, :neval_jac_nln)
   quad_nnzj = nlp.quadcon.nnzj
+  vals .= 0.0
   k = 0
   for i = 1:(nlp.quadcon.nquad)
     qcon = nlp.quadcon[i]
-    vec = qcon.vec
-    for j=1:length(vec)
-      vals[k + j] = qcon.b[j]
+    for j=1:length(qcon.vec)
+      vals[k + j] = qcon.b[qcon.vec[j]]
     end
     nnzj = length(qcon.hessian.vals)
     for i=1:nnzj
-      vals[k + qcon.hessian.rows[i]] += qcon.hessian.vals[i] * x[qcon.hessian.cols[i]]
+      vals[k + i] += qcon.hessian.vals[i] * x[qcon.hessian.cols[i]]
     end
     k += nnzj
   end
@@ -388,6 +388,7 @@ function NLPModels.hess_coord!(
     vals[(nlp.obj.nnzh + 1):(nlp.meta.nnzh)] .= 0.0
   end
   if nlp.obj.type == "NONLINEAR"
+    vals .= 0.0
     MOI.eval_hessian_lagrangian(nlp.eval, vals, x, obj_weight, zeros(nlp.meta.nnln))
   end
 
@@ -407,6 +408,8 @@ function NLPModels.hprod!(
     hv .= 0.0
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
+    ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)
+    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
     for i = 1:(nlp.quadcon.nquad)
       qcon = nlp.quadcon[i]
       for (index,tuple) in enumerate(nlp.quadcon.set)
@@ -414,8 +417,6 @@ function NLPModels.hprod!(
       end
       hv .*= y[nlp.meta.nlin + i]
     end
-    ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)
-    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
   end
   if nlp.obj.type == "QUADRATIC"
     nlp.meta.nnln == 0 && (hv .= 0.0)
diff --git a/test/test_moi_nlp_model.jl b/test/test_moi_nlp_model.jl
index 4f236ba..cd4bb20 100644
--- a/test/test_moi_nlp_model.jl
+++ b/test/test_moi_nlp_model.jl
@@ -23,3 +23,47 @@ for prob in Symbol.(lowercase.(nlp_problems ∪ ["nohesspb", "hs61", "hs100"]))
   @printf("%-15s  %4d  %4d  %10.4e  %10.4e  %10s\n", prob, n, m, fx, ngx, ncx)
 end
 println()
+
+function hs219(args...; kwargs...)
+  nlp = Model()
+  x0 = [10, 10, 10, 10]
+  @variable(nlp, x[i = 1:4], start = x0[i])
+
+  @constraint(nlp, x[1]^2 - x[2] - x[4]^2 == 0)
+  @NLconstraint(nlp, x[2] - x[1]^3 - x[3]^2 == 0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    -x[1]
+  )
+
+  return nlp
+end
+
+@testset "Testing quadratic constraints with JuMP" begin
+  g(x) = [-1., 0., 0., 0.]
+  Hess(x) = zeros(4, 4)
+  function Hess(x, y) 
+    H = zeros(4, 4)
+    H[1, 1] = 2 * y[1] - y[2] * 6 * x[1]
+    H[3, 3] = - 2 * y[2]
+    H[4, 4] = - 2 * y[1]
+    return H
+  end
+  J(x) = [
+      2x[1] -1 0 -2x[4];
+      -3x[1]^2 1 -2x[3] 0
+  ]
+
+  jump = hs219()
+  nlp = MathOptNLPModel(jump)
+  x1 = nlp.meta.x0
+  y1 = ones(nlp.meta.ncon)
+  v1 = 2 * ones(nlp.meta.nvar)
+  @test jac(nlp, x1) ≈ J(x1)
+  @test hess(nlp, x1) ≈ Hess(x1)
+  @test hess(nlp, x1, y1) ≈ Hess(x1, y1)
+  @test hprod(nlp, x1, x1) ≈ Hess(x1) * x1
+  @test hprod(nlp, x1, y1, v1) ≈ Hess(x1, y1) * v1
+end

From 494e3a06acedea776e2446d7c1afc2b6cf362cae Mon Sep 17 00:00:00 2001
From: tmigot <tangi.migot@gmail.com>
Date: Wed, 11 May 2022 15:39:57 +0200
Subject: [PATCH 10/16] only evaluate the NLPEval when there is nonlinear cons

---
 src/moi_nlp_model.jl | 20 +++++++++++++-------
 1 file changed, 13 insertions(+), 7 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index fa9b782..a292cd8 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -120,7 +120,9 @@ function NLPModels.cons_nln!(nlp::MathOptNLPModel, x::AbstractVector, c::Abstrac
     qcon = nlp.quadcon[i]
     c[i] = 0.5 * coo_sym_dot(qcon.hessian.rows, qcon.hessian.cols, qcon.hessian.vals, x, x) + dot(qcon.b, x)
   end
-  MOI.eval_constraint(nlp.eval, view(c, (nlp.quadcon.nquad + 1):(nlp.meta.nnln)), x)
+  if nlp.meta.nnln > nlp.quadcon.nquad
+    MOI.eval_constraint(nlp.eval, view(c, (nlp.quadcon.nquad + 1):(nlp.meta.nnln)), x)
+  end
   return c
 end
 
@@ -142,11 +144,13 @@ function NLPModels.jac_nln_structure!(
   quad_nnzj, jrows, jcols = nlp.quadcon.nnzj, nlp.quadcon.jrows, nlp.quadcon.jcols
   rows[1:quad_nnzj] .= jrows
   cols[1:quad_nnzj] .= jcols
-  jac_struct = MOI.jacobian_structure(nlp.eval)
-  for index =  1:(nlp.meta.nln_nnzj - quad_nnzj)
-    row, col = jac_struct[index]
-    rows[quad_nnzj + index] = row + nlp.quadcon.nquad
-    cols[quad_nnzj + index] = col
+  if nlp.meta.nnln > nlp.quadcon.nquad
+    jac_struct = MOI.jacobian_structure(nlp.eval)
+    for index =  1:(nlp.meta.nln_nnzj - quad_nnzj)
+      row, col = jac_struct[index]
+      rows[quad_nnzj + index] = row + nlp.quadcon.nquad
+      cols[quad_nnzj + index] = col
+    end
   end
   return rows, cols
 end
@@ -173,7 +177,9 @@ function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals:
     end
     k += nnzj
   end
-  MOI.eval_constraint_jacobian(nlp.eval, view(vals, (quad_nnzj + 1):(nlp.meta.nln_nnzj)), x)
+  if nlp.meta.nnln > nlp.quadcon.nquad
+    MOI.eval_constraint_jacobian(nlp.eval, view(vals, (quad_nnzj + 1):(nlp.meta.nln_nnzj)), x)
+  end
   return vals
 end
 

From 01863f70050ebdb297a4f24dc331b2a25560eaf6 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 12 May 2022 19:13:47 -0400
Subject: [PATCH 11/16] =?UTF-8?q?[MathOptNLPModel]=C2=A0Fix=20hprod!?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 src/moi_nlp_model.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index a292cd8..ecc58ec 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -418,10 +418,10 @@ function NLPModels.hprod!(
     MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
     for i = 1:(nlp.quadcon.nquad)
       qcon = nlp.quadcon[i]
-      for (index,tuple) in enumerate(nlp.quadcon.set)
-        hv[tuple[1]] += qcon.hessian.vals[index] * v[tuple[2]]
+      for k = 1:length(qcon.hessian.vals)
+        hv[qcon.hessian.rows[k]] += qcon.hessian.vals[k] * v[qcon.hessian.cols[k]
       end
-      hv .*= y[nlp.meta.nlin + i]
+      hv[i] *= obj_weight * y[nlp.meta.nlin + i]
     end
   end
   if nlp.obj.type == "QUADRATIC"

From 86ccf4438e0c1307694df4a61fa68e36fe732c38 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 12 May 2022 19:32:25 -0400
Subject: [PATCH 12/16] =?UTF-8?q?[MathOptNLPModel]=C2=A0Fix=20cases=20with?=
 =?UTF-8?q?=20nlp.eval=20=3D=3D=20nothing?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 src/moi_nlp_model.jl | 38 ++++++++++++++++++++++----------------
 1 file changed, 22 insertions(+), 16 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index ecc58ec..40cfc02 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -333,16 +333,19 @@ function NLPModels.hess_structure!(
       cols[index] = nlp.obj.hessian.cols[index]
     end
   end
-  if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
+  if nlp.quadcon.nquad > 0
     quad_nnzh = nlp.quadcon.nnzh
     hrows, hcols = hessian_structure(nlp.quadcon.set)
     rows[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= hrows
     cols[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= hcols
-    hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)
-    for index = (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)
-      shift_index = index - nlp.obj.nnzh - quad_nnzh
-      rows[index] = hesslag_struct[shift_index][1]
-      cols[index] = hesslag_struct[shift_index][2]
+  end
+  if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
+      hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)
+      for index = (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)
+        shift_index = index - nlp.obj.nnzh - quad_nnzh
+        rows[index] = hesslag_struct[shift_index][1]
+        cols[index] = hesslag_struct[shift_index][2]
+      end
     end
   end
   return rows, cols
@@ -359,7 +362,7 @@ function NLPModels.hess_coord!(
   if nlp.obj.type == "QUADRATIC"
     vals[1:(nlp.obj.nnzh)] .= obj_weight .* nlp.obj.hessian.vals
   end
-  if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
+  if nlp.quadcon.nquad > 0
     quad_nnzh = nlp.quadcon.nnzh
     k = 0
     for i = 1:(nlp.quadcon.nquad)
@@ -368,12 +371,14 @@ function NLPModels.hess_coord!(
       vals[(k + 1):(k + nnzh)] .= qcon.hessian.vals .* y[nlp.meta.nlin + i]
       k += nnzh
     end
+  end
+  if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
     MOI.eval_hessian_lagrangian(
       nlp.eval,
       view(vals, (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)),
       x,
       obj_weight,
-      view(y, (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)),
+      view(y, (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon))
     )
   end
   return vals
@@ -413,16 +418,17 @@ function NLPModels.hprod!(
   if (nlp.obj.type == "LINEAR") && (nlp.meta.nnln == 0)
     hv .= 0.0
   end
-  if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > 0)
-    ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)
-    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
+  if nlp.quadcon.nquad > 0
     for i = 1:(nlp.quadcon.nquad)
-      qcon = nlp.quadcon[i]
-      for k = 1:length(qcon.hessian.vals)
-        hv[qcon.hessian.rows[k]] += qcon.hessian.vals[k] * v[qcon.hessian.cols[k]
-      end
-      hv[i] *= obj_weight * y[nlp.meta.nlin + i]
+    qcon = nlp.quadcon[i]
+    for k = 1:length(qcon.hessian.vals)
+      hv[qcon.hessian.rows[k]] += qcon.hessian.vals[k] * v[qcon.hessian.cols[k]]
     end
+    hv[i] *= obj_weight * y[nlp.meta.nlin + i]
+  end
+  if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
+    ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)
+    MOI.eval_hessian_lagrangian_product(nlp.eval, hv, x, v, obj_weight, view(y, ind_nln))
   end
   if nlp.obj.type == "QUADRATIC"
     nlp.meta.nnln == 0 && (hv .= 0.0)

From ef957701624e926610ce9aacdaf35bec96cd49a8 Mon Sep 17 00:00:00 2001
From: Alexis <35051714+amontoison@users.noreply.github.com>
Date: Thu, 12 May 2022 19:36:11 -0400
Subject: [PATCH 13/16] Update test/nlp_problems/hs100.jl

---
 test/nlp_problems/hs100.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/nlp_problems/hs100.jl b/test/nlp_problems/hs100.jl
index 2dca312..b4af448 100644
--- a/test/nlp_problems/hs100.jl
+++ b/test/nlp_problems/hs100.jl
@@ -21,4 +21,4 @@ function hs100(args...; kwargs...)
   )
 
   return nlp
-end
\ No newline at end of file
+end

From c64ac7421aa4a598fa7ae6e89e40348069d8ab71 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 12 May 2022 19:41:30 -0400
Subject: [PATCH 14/16] Remove hessian_structure function

---
 src/utils.jl | 11 -----------
 1 file changed, 11 deletions(-)

diff --git a/src/utils.jl b/src/utils.jl
index bfa0842..12913be 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -166,17 +166,6 @@ function hessian_quad(qcons)
   return set
 end
 
-function hessian_structure(set)
-  nnzh = length(set)
-  hrows = zeros(Int, nnzh)
-  hcols = zeros(Int, nnzh)
-  for (index,tuple) in enumerate(set)
-    hrows[index] = tuple[1]
-    hcols[index] = tuple[2]
-  end
-  return hrows, hcols
-end
-
 """
     parser_SAF(fun, set, linrows, lincols, linvals, nlin, lin_lcon, lin_ucon)
 

From 4b24cab04d99e5b99b95040ffe8dc03f5626df0a Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 12 May 2022 19:42:04 -0400
Subject: [PATCH 15/16] Optimize hessian_structure function for quadratic
 constraints

---
 src/moi_nlp_model.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index 40cfc02..eea3e57 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -334,10 +334,10 @@ function NLPModels.hess_structure!(
     end
   end
   if nlp.quadcon.nquad > 0
-    quad_nnzh = nlp.quadcon.nnzh
-    hrows, hcols = hessian_structure(nlp.quadcon.set)
-    rows[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= hrows
-    cols[(1 + nlp.obj.nnzh):(nlp.obj.nnzh + quad_nnzh)] .= hcols
+    for (index, tuple) in enumerate(nlp.quadcon.set)
+      rows[nlp.obj.nnzh + index] = tuple[1]
+      cols[nlp.obj.nnzh + index] = tuple[2]
+    end
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
       hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)

From e141a9c0b4df1828ba00147e81bc09c93c1a18b6 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 12 May 2022 20:00:15 -0400
Subject: [PATCH 16/16] [MathOptNLPModel] hotfix

---
 src/moi_nlp_model.jl | 25 ++++++++++++-------------
 1 file changed, 12 insertions(+), 13 deletions(-)

diff --git a/src/moi_nlp_model.jl b/src/moi_nlp_model.jl
index eea3e57..682f5ad 100644
--- a/src/moi_nlp_model.jl
+++ b/src/moi_nlp_model.jl
@@ -163,7 +163,6 @@ end
 
 function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals::AbstractVector)
   increment!(nlp, :neval_jac_nln)
-  quad_nnzj = nlp.quadcon.nnzj
   vals .= 0.0
   k = 0
   for i = 1:(nlp.quadcon.nquad)
@@ -178,7 +177,7 @@ function NLPModels.jac_nln_coord!(nlp::MathOptNLPModel, x::AbstractVector, vals:
     k += nnzj
   end
   if nlp.meta.nnln > nlp.quadcon.nquad
-    MOI.eval_constraint_jacobian(nlp.eval, view(vals, (quad_nnzj + 1):(nlp.meta.nln_nnzj)), x)
+    MOI.eval_constraint_jacobian(nlp.eval, view(vals, (nlp.quadcon.nnzj + 1):(nlp.meta.nln_nnzj)), x)
   end
   return vals
 end
@@ -340,12 +339,11 @@ function NLPModels.hess_structure!(
     end
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
-      hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)
-      for index = (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)
-        shift_index = index - nlp.obj.nnzh - quad_nnzh
-        rows[index] = hesslag_struct[shift_index][1]
-        cols[index] = hesslag_struct[shift_index][2]
-      end
+    hesslag_struct = MOI.hessian_lagrangian_structure(nlp.eval)
+    for index = (nlp.obj.nnzh + nlp.quadcon.nnzh + 1):(nlp.meta.nnzh)
+      shift_index = index - nlp.obj.nnzh - nlp.quadcon.nnzh
+      rows[index] = hesslag_struct[shift_index][1]
+      cols[index] = hesslag_struct[shift_index][2]
     end
   end
   return rows, cols
@@ -375,7 +373,7 @@ function NLPModels.hess_coord!(
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
     MOI.eval_hessian_lagrangian(
       nlp.eval,
-      view(vals, (nlp.obj.nnzh + quad_nnzh + 1):(nlp.meta.nnzh)),
+      view(vals, (nlp.obj.nnzh + nlp.quadcon.nnzh + 1):(nlp.meta.nnzh)),
       x,
       obj_weight,
       view(y, (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon))
@@ -420,11 +418,12 @@ function NLPModels.hprod!(
   end
   if nlp.quadcon.nquad > 0
     for i = 1:(nlp.quadcon.nquad)
-    qcon = nlp.quadcon[i]
-    for k = 1:length(qcon.hessian.vals)
-      hv[qcon.hessian.rows[k]] += qcon.hessian.vals[k] * v[qcon.hessian.cols[k]]
+      qcon = nlp.quadcon[i]
+      for k = 1:length(qcon.hessian.vals)
+        hv[qcon.hessian.rows[k]] += qcon.hessian.vals[k] * v[qcon.hessian.cols[k]]
+      end
+      hv[i] *= y[nlp.meta.nlin + i]
     end
-    hv[i] *= obj_weight * y[nlp.meta.nlin + i]
   end
   if (nlp.obj.type == "NONLINEAR") || (nlp.meta.nnln > nlp.quadcon.nquad)
     ind_nln = (nlp.meta.nlin + nlp.quadcon.nquad + 1):(nlp.meta.ncon)