Add VectorNonlinearFunction (#2201)

Author: odow

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