diff --git a/src/Bridges/Constraint/interval.jl b/src/Bridges/Constraint/interval.jl
index 29e99313f4..d6a7a82c0c 100644
--- a/src/Bridges/Constraint/interval.jl
+++ b/src/Bridges/Constraint/interval.jl
@@ -1,5 +1,5 @@
-_lower_set(set::MOI.Interval) = MOI.GreaterThan(set.lower)
-_upper_set(set::MOI.Interval) = MOI.LessThan(set.upper)
+_lower_set(set::MOI.Interval) = isinf(set.lower) ? MOI.ExtendedGreaterThan(set.lower) : MOI.GreaterThan(set.lower)
+_upper_set(set::MOI.Interval) = isinf(set.upper) ? MOI.ExtendedLessThan(set.upper) : MOI.LessThan(set.upper)
 _lower_set(set::MOI.EqualTo) = MOI.GreaterThan(set.value)
 _upper_set(set::MOI.EqualTo) = MOI.LessThan(set.value)
 _lower_set(set::MOI.Zeros) = MOI.Nonnegatives(set.dimension)
@@ -267,3 +267,31 @@ function MOI.get(
 ) where {T,F}
     return MOI.Zeros(MOI.get(model, attr, bridge.lower).dimension)
 end
+
+
+# guimarqu : new bridge (to improve)
+"""
+    UnextendBridge
+
+Bridge for ExtendedGreatherThan to GreaterThan ...
+"""
+struct UnextendBridge{
+    T,
+    F<:MOI.AbstractFunction,
+    ES<:MOI.AbstractSet,
+    S<:MOI.AbstractSet
+} <: AbstractBridge
+    non_extended::Union{Nothing, CI{F,S}}
+end
+
+function bridge_constraint(
+    ::Type{UnextendBridge{T,F,ES,S}},
+    model::MOI.ModelLike,
+    f::F,
+    set::S,
+) where {T,F,ES,S}
+    if isinf(set.value)
+        return UnextendBridge{T,F,ES,S}(nothing)
+    end
+    return UnextendBridge{T,F,ES,S}(MOI.GreaterThan(3))
+end
diff --git a/src/Test/UnitTests/constraints.jl b/src/Test/UnitTests/constraints.jl
index 1788b96474..8019479fa2 100644
--- a/src/Test/UnitTests/constraints.jl
+++ b/src/Test/UnitTests/constraints.jl
@@ -521,3 +521,54 @@ function solve_zero_one_with_bounds_3(model::MOI.ModelLike, config::TestConfig)
     end
 end
 unittests["solve_zero_one_with_bounds_3"] = solve_zero_one_with_bounds_3
+
+function solve_one_sided_intervals(model::MOI.ModelLike, config::TestConfig)
+    MOI.empty!(model)
+    MOIU.loadfromstring!(
+        model,
+        """
+    variables: x, y, z
+    maxobjective: x + -1y + z
+    c1: x in Interval(-Inf, 1.0)
+    c2: y in Interval(-1.0, Inf)
+    c3: z in Interval(-Inf, Inf)
+    c4: 1z <= 1.0
+""",
+    )
+
+    x = MOI.get(model, MOI.VariableIndex, "x")
+    y = MOI.get(model, MOI.VariableIndex, "y")
+    z = MOI.get(model, MOI.VariableIndex, "z")
+
+    c1 = MOI.get(
+        model,
+        MOI.ConstraintIndex{MOI.SingleVariable, MOI.Interval{Float64}},
+        "c1"
+    )
+    c2 = MOI.get(
+        model,
+        MOI.ConstraintIndex{MOI.SingleVariable, MOI.Interval{Float64}},
+        "c2"
+    )
+    c3 = MOI.get(
+        model,
+        MOI.ConstraintIndex{MOI.SingleVariable, MOI.Interval{Float64}},
+        "c3"
+    )
+
+    @test MOI.get(model, MOI.ConstraintIndex, "c1") == c1
+    @test MOI.get(model, MOI.ConstraintIndex, "c2") == c2
+    @test MOI.get(model, MOI.ConstraintIndex, "c3") == c3
+    
+    @test MOI.is_valid(model, c1)
+    @test MOI.is_valid(model, c2)
+    @test MOI.is_valid(model, c3)
+
+    return test_model_solution(
+        model,
+        config;
+        objective_value = 3.0,
+        variable_primal = [(x, 1.0), (y, -1.0), (z, 1.0)],
+    )
+end
+unittests["solve_one_sided_intervals"] = solve_one_sided_intervals
\ No newline at end of file
diff --git a/src/sets.jl b/src/sets.jl
index 2b8772d500..ba935365c7 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -162,6 +162,11 @@ struct GreaterThan{T<:Real} <: AbstractScalarSet
     lower::T
 end
 
+# guimarqu
+struct ExtendedGreaterThan{T<:Real} <: AbstractScalarSet
+    lower::T
+end
+
 """
     LessThan{T <: Real}(upper::T)
 
@@ -171,6 +176,11 @@ struct LessThan{T<:Real} <: AbstractScalarSet
     upper::T
 end
 
+# guimarqu
+struct ExtendedLessThan{T<:Real} <: AbstractScalarSet
+    lower::T
+end
+
 """
     EqualTo{T <: Number}(value::T)
 
diff --git a/test/Bridges/Constraint/interval.jl b/test/Bridges/Constraint/interval.jl
index 2635522e9a..d444efe91e 100644
--- a/test/Bridges/Constraint/interval.jl
+++ b/test/Bridges/Constraint/interval.jl
@@ -12,6 +12,7 @@ mock = MOIU.MockOptimizer(MOIU.UniversalFallback(MOIU.Model{Float64}()))
 config = MOIT.TestConfig()
 config_with_basis = MOIT.TestConfig(basis = true)
 
+
 @testset "Split" begin
     T = Float64
     bridged_mock = MOIB.Constraint.SplitInterval{T}(mock)
@@ -32,6 +33,46 @@ config_with_basis = MOIT.TestConfig(basis = true)
     )
 end
 
+@testset "my test" begin
+    bridged_mock = MOIB.Constraint.SplitInterval{Float64}(mock)
+
+    MOIU.set_mock_optimize!(
+        mock,
+        (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(
+            mock,
+            [1.0, -1.0, 1.0],
+        ),
+    )
+
+    # variables: x, y, z
+    # maxobjective: x + -1y + z
+    # c1: x in Interval(-Inf, 1.0)
+    # c2: y in Interval(-1.0, Inf)
+    # c3: z in Interval(-Inf, Inf)
+    # c4: 1z <= 1.0
+    MOIT.solve_one_sided_intervals(bridged_mock, config_with_basis)
+
+    println("====== ****** ======")
+    for (i, b) in bridged_mock.map.single_variable_constraints
+        @show MOI.get(bridged_mock.model, MOI.ConstraintSet(), b.lower)
+        @show MOI.get(bridged_mock.model, MOI.ConstraintSet(), b.upper)
+    end
+
+    println("====== ****** ======")
+
+    @show MOI.get(
+            bridged_mock,
+            MOI.ListOfConstraintIndices{
+                MOI.SingleVariable,
+                MOI.Interval{Float64},
+            }(),
+        )
+
+    
+    
+end
+exit()
+
 @testset "Interval" begin
     bridged_mock = MOIB.Constraint.SplitInterval{Float64}(mock)
     MOIU.set_mock_optimize!(
diff --git a/test/Test/unit.jl b/test/Test/unit.jl
index 6b62fee2c9..398000e9aa 100644
--- a/test/Test/unit.jl
+++ b/test/Test/unit.jl
@@ -53,6 +53,7 @@ end
                 "solve_zero_one_with_bounds_1",
                 "solve_zero_one_with_bounds_2",
                 "solve_zero_one_with_bounds_3",
+                "solve_one_sided_intervals",
                 "solve_unbounded_model",
                 "solve_single_variable_dual_min",
                 "solve_single_variable_dual_max",
@@ -447,6 +448,22 @@ end
         MOIT.solve_zero_one_with_bounds_3(mock, config)
     end
 
+    @testset "solve_one_sided_intervals" begin
+        MOIU.set_mock_optimize!(mock,
+            (mock::MOIU.MockOptimizer) -> begin
+                MOIU.mock_optimize!(
+                    mock, MOI.OPTIMAL, (MOI.FEASIBLE_POINT, [1.0, -1.0])
+                )
+            end,
+            (mock::MOIU.MockOptimizer) -> begin
+                MOIU.mock_optimize!(
+                    mock, MOI.OPTIMAL, (MOI.FEASIBLE_POINT, [1.0, -1.0, 1.0])
+                )
+            end
+        )
+        MOIT.solve_one_sided_intervals(mock, config)
+    end
+
     @testset "solve_unbounded_model" begin
         MOIU.set_mock_optimize!(
             mock,