Add VectorNonlinearFunction (#2201)

docs/src/manual/standard_form.md

@@ -41,6 +41,7 @@ The function types implemented in MathOptInterface.jl are:
 | [`VectorAffineFunction`](@ref) | ``A x + b``, where ``A`` is a matrix and ``b`` is a vector. |
 | [`ScalarQuadraticFunction`](@ref) | ``\frac{1}{2} x^T Q x + a^T x + b``, where ``Q`` is a symmetric matrix, ``a`` is a vector, and ``b`` is a constant. |
 | [`VectorQuadraticFunction`](@ref) | A vector of scalar-valued quadratic functions. |
+| [`VectorNonlinearFunction`](@ref) | ``f(x)``, where ``f`` is a vector-valued nonlinear function. |
 
 Extensions for nonlinear programming are present but not yet well documented.
 

docs/src/reference/standard_form.md

@@ -37,6 +37,7 @@ VectorAffineTerm
 VectorAffineFunction
 VectorQuadraticTerm
 VectorQuadraticFunction
+VectorNonlinearFunction
 ```
 
 ## Sets

src/Bridges/Constraint/bridges/square.jl

@@ -76,6 +76,58 @@ _square_offset(::MOI.AbstractSymmetricMatrixSetSquare) = Int[]
 _square_offset(::MOI.RootDetConeSquare) = Int[1]
 _square_offset(::MOI.LogDetConeSquare) = Int[1, 2]
 
+function _constrain_off_diagonals(
+ model::MOI.ModelLike,
+ ::Type{T},
+ ::Tuple{Int,Int},
+ f_ij::F,
+ f_ji::F,
+) where {T,F<:MOI.ScalarNonlinearFunction}
+ if isapprox(f_ij, f_ji)
+ return nothing
+ end
+ return MOI.Utilities.normalize_and_add_constraint(
+ model,
+ MOI.ScalarNonlinearFunction(:-, Any[f_ij, f_ji]),
+ MOI.EqualTo(zero(T));
+ allow_modify_function = true,
+ )
+end
+
+function _constrain_off_diagonals(
+ model::MOI.ModelLike,
+ ::Type{T},
+ ij::Tuple{Int,Int},
+ f_ij::F,
+ f_ji::F,
+) where {T,F}
+ diff = MOI.Utilities.operate!(-, T, f_ij, f_ji)
+ MOI.Utilities.canonicalize!(diff)
+ # The value 1e-10 was decided in https://github.com/jump-dev/JuMP.jl/pull/976
+ # This avoid generating symmetrization constraints when the
+ # functions at entries (i, j) and (j, i) are almost identical
+ if MOI.Utilities.isapprox_zero(diff, 1e-10)
+ return nothing
+ end
+ if MOI.Utilities.isapprox_zero(diff, 1e-8)
+ i, j = ij
+ @warn(
+ "The entries ($i, $j) and ($j, $i) of the matrix are " *
+ "almost identical, but a constraint has been added " *
+ "to ensure their equality because the largest " *
+ "difference between the coefficients is smaller than " *
+ "1e-8 but larger than 1e-10. This usually means that " *
+ "there is a modeling error in your formulation.",
+ )
+ end
+ return MOI.Utilities.normalize_and_add_constraint(
+ model,
+ diff,
+ MOI.EqualTo(zero(T));
+ allow_modify_function = true,
+ )
+end
+
 function bridge_constraint(
  ::Type{SquareBridge{T,F,G,TT,ST}},
  model::MOI.ModelLike,
@@ -93,32 +145,14 @@ function bridge_constraint(
  for i in 1:j
  k += 1
  push!(upper_triangle_indices, k)
- # We constrain the entries (i, j) and (j, i) to be equal
- f_ij = f_scalars[offset+i+(j-1)*dim]
- f_ji = f_scalars[offset+j+(i-1)*dim]
- diff = MOI.Utilities.operate!(-, T, f_ij, f_ji)
- MOI.Utilities.canonicalize!(diff)
- # The value 1e-10 was decided in https://github.com/jump-dev/JuMP.jl/pull/976
- # This avoid generating symmetrization constraints when the
- # functions at entries (i, j) and (j, i) are almost identical
- if !MOI.Utilities.isapprox_zero(diff, 1e-10)
- if MOI.Utilities.isapprox_zero(diff, 1e-8)
- @warn(
- "The entries ($i, $j) and ($j, $i) of the matrix are " *
- "almost identical, but a constraint has been added " *
- "to ensure their equality because the largest " *
- "difference between the coefficients is smaller than " *
- "1e-8 but larger than 1e-10. This usually means that " *
- "there is a modeling error in your formulation.",
- )
+ if i !== j
+ # We constrain the entries (i, j) and (j, i) to be equal
+ f_ij = f_scalars[offset+i+(j-1)*dim]
+ f_ji = f_scalars[offset+j+(i-1)*dim]
+ ci = _constrain_off_diagonals(model, T, (i, j), f_ij, f_ji)
+ if ci !== nothing
+ push!(sym, (i, j) => ci)
  end
- ci = MOI.Utilities.normalize_and_add_constraint(
- model,
- diff,
- MOI.EqualTo(zero(T));
- allow_modify_function = true,
- )
- push!(sym, (i, j) => ci)
  end
  end
  k += dim - j

src/Bridges/Constraint/bridges/vectorize.jl

@@ -67,14 +67,6 @@ function MOI.supports_constraint(
  return true
 end
 
-function MOI.supports_constraint(
- ::Type{VectorizeBridge{T}},
- ::Type{MOI.ScalarNonlinearFunction},
- ::Type{<:MOI.Utilities.ScalarLinearSet{T}},
-) where {T}
- return false
-end
-
 function MOI.Bridges.added_constrained_variable_types(::Type{<:VectorizeBridge})
  return Tuple{Type}[]
 end

src/Test/test_basic_constraint.jl

@@ -77,6 +77,18 @@ function _function(
  )
 end
 
+function _function(
+ ::Type{T},
+ ::Type{MOI.VectorNonlinearFunction},
+ x::Vector{MOI.VariableIndex},
+) where {T}
+ f = MOI.ScalarNonlinearFunction(
+ :+,
+ Any[MOI.ScalarNonlinearFunction(:^, Any[xi, 2]) for xi in x],
+ )
+ return MOI.VectorNonlinearFunction([f; x])
+end
+
 # Default fallback.
 _set(::Any, ::Type{S}) where {S} = _set(S)
 
@@ -334,7 +346,12 @@ for s in [
  :ScalarNonlinearFunction,
  )
  else
- (:VectorOfVariables, :VectorAffineFunction, :VectorQuadraticFunction)
+ (
+ :VectorOfVariables,
+ :VectorAffineFunction,
+ :VectorQuadraticFunction,
+ :VectorNonlinearFunction,
+ )
  end
  for f in functions
  func = Symbol("test_basic_$(f)_$(s)")

src/Test/test_multiobjective.jl

@@ -228,3 +228,82 @@ function test_multiobjective_vector_quadratic_function_delete_vector(
  @test MOI.get(model, MOI.ObjectiveFunction{F}()) ≈ new_f
  return
 end
+
+function test_multiobjective_vector_nonlinear(
+ model::MOI.ModelLike,
+ ::Config{T},
+) where {T}
+ F = MOI.VectorNonlinearFunction
+ @requires MOI.supports(model, MOI.ObjectiveFunction{F}())
+ x = MOI.add_variables(model, 2)
+ MOI.add_constraint.(model, x, MOI.GreaterThan(T(0)))
+ f = MOI.VectorNonlinearFunction(
+ Any[MOI.ScalarNonlinearFunction(:^, Any[x[1], 2]), x[2]],
+ ) # [x[1]^2, x[2]]
+ MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+ MOI.set(model, MOI.ObjectiveFunction{F}(), f)
+ @test MOI.get(model, MOI.ObjectiveFunctionType()) == F
+ @test MOI.get(model, MOI.ObjectiveFunction{F}()) ≈ f
+ return
+end
+
+function test_multiobjective_vector_nonlinear_delete(
+ model::MOI.ModelLike,
+ ::Config{T},
+) where {T}
+ F = MOI.VectorNonlinearFunction
+ @requires MOI.supports(model, MOI.ObjectiveFunction{F}())
+ x = MOI.add_variables(model, 2)
+ MOI.add_constraint.(model, x, MOI.GreaterThan(T(0)))
+ f = MOI.VectorNonlinearFunction(
+ Any[MOI.ScalarNonlinearFunction(:^, Any[x[1], 2]), x[2]],
+ ) # [x[1]^2, x[2]]
+ MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+ MOI.set(model, MOI.ObjectiveFunction{F}(), f)
+ @test MOI.get(model, MOI.ObjectiveFunctionType()) == F
+ @test MOI.get(model, MOI.ObjectiveFunction{F}()) ≈ f
+ @test_throws MOI.DeleteNotAllowed MOI.delete(model, x[1])
+ return
+end
+
+function test_multiobjective_vector_nonlinear_delete_vector(
+ model::MOI.ModelLike,
+ ::Config{T},
+) where {T}
+ F = MOI.VectorNonlinearFunction
+ @requires MOI.supports(model, MOI.ObjectiveFunction{F}())
+ x = MOI.add_variables(model, 2)
+ MOI.add_constraint.(model, x, MOI.GreaterThan(T(0)))
+ f = MOI.VectorNonlinearFunction(
+ Any[MOI.ScalarNonlinearFunction(:^, Any[x[1], 2]), x[2]],
+ ) # [x[1]^2, x[2]]
+ MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+ MOI.set(model, MOI.ObjectiveFunction{F}(), f)
+ @test MOI.get(model, MOI.ObjectiveFunctionType()) == F
+ @test MOI.get(model, MOI.ObjectiveFunction{F}()) ≈ f
+ @test_throws MOI.DeleteNotAllowed MOI.delete(model, x)
+ return
+end
+
+function test_multiobjective_vector_nonlinear_modify(
+ model::MOI.ModelLike,
+ ::Config{T},
+) where {T}
+ F = MOI.VectorNonlinearFunction
+ attr = MOI.ObjectiveFunction{F}()
+ @requires MOI.supports(model, attr)
+ x = MOI.add_variables(model, 2)
+ MOI.add_constraint.(model, x, MOI.GreaterThan(T(0)))
+ f = MOI.VectorNonlinearFunction(
+ Any[MOI.ScalarNonlinearFunction(:^, Any[x[1], 2]), x[2]],
+ ) # [x[1]^2, x[2]]
+ MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+ MOI.set(model, attr, f)
+ @test MOI.get(model, MOI.ObjectiveFunctionType()) == F
+ @test MOI.get(model, attr) ≈ f
+ @test_throws(
+ MOI.ModifyObjectiveNotAllowed,
+ MOI.modify(model, attr, MOI.VectorConstantChange(T[1, 2])),
+ )
+ return
+end

src/Test/test_nonlinear.jl

@@ -1673,3 +1673,93 @@ function setup_test(
  model.eval_objective_value = obj_flag
  end
 end
+
+function test_nonlinear_vector_complements(
+ model::MOI.ModelLike,
+ config::MOI.Test.Config{T},
+) where {T}
+ @requires T == Float64
+ @requires _supports(config, MOI.optimize!)
+ F = MOI.ScalarNonlinearFunction
+ @requires MOI.supports_constraint(model, F, MOI.Complements)
+ x = MOI.add_variables(model, 4)
+ MOI.add_constraint.(model, x, MOI.Interval(T(0), T(10)))
+ MOI.set.(model, MOI.VariablePrimalStart(), x, T(1))
+ # f = [
+ # -1 * x3^2 + -1 * x4 + 2.0
+ # x3^3 + -1.0 * 2x4^2 + 2.0
+ # x1^5 + -1.0 * x2 + 2.0 * x3 + -2.0 * x4 + -2.0
+ # x1 + 2.0 * x2^3 + -2.0 * x3 + 4.0 * x4 + -6.0
+ # x...
+ # ]
+ f = MOI.VectorNonlinearFunction([
+ MOI.ScalarNonlinearFunction(
+ :+,
+ Any[
+ MOI.ScalarNonlinearFunction(:*, Any[-T(1), x[3], x[3]]),
+ MOI.ScalarNonlinearFunction(:*, Any[-T(1), x[4]]),
+ T(2),
+ ],
+ ),
+ MOI.ScalarNonlinearFunction(
+ :+,
+ Any[
+ MOI.ScalarNonlinearFunction(:^, Any[x[3], 3]),
+ MOI.ScalarNonlinearFunction(:*, Any[-T(2), x[4], x[4]]),
+ T(2),
+ ],
+ ),
+ MOI.ScalarNonlinearFunction(
+ :+,
+ Any[
+ MOI.ScalarNonlinearFunction(:^, Any[x[1], 5]),
+ MOI.ScalarAffineFunction{T}(
+ MOI.ScalarAffineTerm.(T[-1, 2, -2], x[2:4]),
+ -T(2),
+ ),
+ ],
+ ),
+ MOI.ScalarNonlinearFunction(
+ :+,
+ Any[
+ MOI.ScalarNonlinearFunction(:*, Any[T(2), x[2], x[2], x[2]]),
+ MOI.ScalarAffineFunction{T}(
+ MOI.ScalarAffineTerm.(T[1, -2, 4], [x[1], x[3], x[4]]),
+ -T(6),
+ ),
+ ],
+ ),
+ x[1],
+ x[2],
+ x[3],
+ x[4],
+ ])
+ MOI.add_constraint(model, f, MOI.Complements(8))
+ MOI.optimize!(model)
+ @test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
+ @test ≈(
+ MOI.get.(model, MOI.VariablePrimal(), x),
+ T[1.2847523, 0.9729165, 0.9093762, 1.1730350],
+ config,
+ )
+ return
+end
+
+function setup_test(
+ ::typeof(test_nonlinear_vector_complements),
+ model::MOIU.MockOptimizer,
+ config::Config{T},
+) where {T}
+ if T != Float64
+ return # Skip for non-Float64 solvers
+ end
+ MOI.Utilities.set_mock_optimize!(
+ model,
+ mock -> MOI.Utilities.mock_optimize!(
+ mock,
+ config.optimal_status,
+ T[1.2847523, 0.9729165, 0.9093762, 1.1730350],
+ ),
+ )
+ return
+end