diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index 5cf614923..293946710 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -8,6 +8,7 @@ struct Optimizer{T,M} <: MOI.AbstractOptimizer
     moi_to_convex::OrderedCollections.OrderedDict{MOI.VariableIndex,Any}
     convex_to_moi::Dict{UInt64,Vector{MOI.VariableIndex}}
     constraint_map::Vector{MOI.ConstraintIndex}
+
     function Optimizer(context::Context{T,M}) where {T,M}
         return new{T,M}(
             context,
@@ -211,6 +212,10 @@ function MOI.add_constraint(
     set::MOI.AbstractVectorSet,
 ) where {T}
     constraint = Constraint(_expr(model, func), set)
+    if vexity(constraint) == Convex.NotDcp()
+        msg = "\n\n[Convex.jl] The constraint is not convex according to the axioms of Disciplined Convex Programming.\n\n"
+        throw(MOI.AddConstraintNotAllowed{typeof(func),typeof(set)}(msg))
+    end
     add_constraint!(model.context, constraint)
     push!(model.constraint_map, model.context.constr_to_moi_inds[constraint])
     return MOI.ConstraintIndex{typeof(func),typeof(set)}(
@@ -231,10 +236,19 @@ end
 
 function MOI.set(
     model::Optimizer{T},
-    ::MOI.ObjectiveFunction{MOI.ScalarNonlinearFunction},
+    attr::MOI.ObjectiveFunction{MOI.ScalarNonlinearFunction},
     func::MOI.ScalarNonlinearFunction,
 ) where {T}
-    cfp = conic_form!(model.context, _expr(model, func))
+    obj_fn = _expr(model, func)
+    vex = vexity(obj_fn)
+    if MOI.get(model, MOI.ObjectiveSense()) == MOI.MAX_SENSE
+        vex = -vex
+    end
+    if vex in (Convex.NotDcp(), Convex.ConcaveVexity())
+        msg = "\n\n[Convex.jl] The objective is not convex according to the axioms of Disciplined Convex Programming.\n\n"
+        throw(MOI.SetAttributeNotAllowed(attr, msg))
+    end
+    cfp = conic_form!(model.context, obj_fn)
     obj = _to_scalar_moi(T, cfp)
     MOI.set(model, MOI.ObjectiveFunction{typeof(obj)}(), obj)
     return
diff --git a/test/MOI_wrapper.jl b/test/MOI_wrapper.jl
index 8a4e4b207..66f8c7dd5 100644
--- a/test/MOI_wrapper.jl
+++ b/test/MOI_wrapper.jl
@@ -108,6 +108,60 @@ function test_scalar_nonlinear_function()
     return
 end
 
+function test_not_dcp_constraint()
+    inner = Convex.Optimizer(ECOS.Optimizer)
+    model = MOI.Utilities.CachingOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
+        MOI.Bridges.full_bridge_optimizer(inner, Float64),
+    )
+    x = MOI.add_variable(model)
+    f = MOI.ScalarNonlinearFunction(:^, Any[x, 2])
+    MOI.add_constraint(model, f, MOI.GreaterThan(1.0))
+    F, S = MOI.VectorNonlinearFunction, MOI.Nonnegatives
+    @test_throws(
+        MOI.AddConstraintNotAllowed{F,S},
+        MOI.Utilities.attach_optimizer(model),
+    )
+    return
+end
+
+function test_not_dcp_objective()
+    inner = Convex.Optimizer(ECOS.Optimizer)
+    model = MOI.Utilities.CachingOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
+        MOI.Bridges.full_bridge_optimizer(inner, Float64),
+    )
+    x = MOI.add_variable(model)
+    f = MOI.ScalarNonlinearFunction(:^, Any[x, 2])
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+    attr = MOI.ObjectiveFunction{typeof(f)}()
+    MOI.set(model, attr, f)
+    @test_throws(
+        MOI.SetAttributeNotAllowed{typeof(attr)},
+        MOI.Utilities.attach_optimizer(model),
+    )
+    return
+end
+
+function test_not_dcp_objective_min()
+    inner = Convex.Optimizer(ECOS.Optimizer)
+    model = MOI.Utilities.CachingOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
+        MOI.Bridges.full_bridge_optimizer(inner, Float64),
+    )
+    x = MOI.add_variable(model)
+    g = MOI.ScalarNonlinearFunction(:^, Any[x, 2])
+    f = MOI.ScalarNonlinearFunction(:-, Any[g])
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    attr = MOI.ObjectiveFunction{typeof(f)}()
+    MOI.set(model, attr, f)
+    @test_throws(
+        MOI.SetAttributeNotAllowed{typeof(attr)},
+        MOI.Utilities.attach_optimizer(model),
+    )
+    return
+end
+
 end  # TestMOIWrapper
 
 TestMOIWrapper.runtests()