diff --git a/REQUIRE b/REQUIRE
index b62a93944c4..7ab83d8feb6 100644
--- a/REQUIRE
+++ b/REQUIRE
@@ -1,5 +1,5 @@
 julia 0.7
-MathOptInterface 0.6.3 0.7
+MathOptInterface 0.7 0.8
 ForwardDiff 0.5 0.11
 Calculus
 DataStructures
diff --git a/docs/src/quickstart.md b/docs/src/quickstart.md
index 35500114ba5..7c4986fdf88 100644
--- a/docs/src/quickstart.md
+++ b/docs/src/quickstart.md
@@ -99,7 +99,7 @@ DocTestSetup = quote
     # Now we load in the solution. Using a caching optimizer removes the need to
     # load a solver such as GLPK for building the documentation.
     mock = JuMP.backend(model).optimizer.model
-    MOI.set(mock, MOI.TerminationStatus(), MOI.Success)
+    MOI.set(mock, MOI.TerminationStatus(), MOI.Optimal)
     MOI.set(mock, MOI.PrimalStatus(), MOI.FeasiblePoint)
     MOI.set(mock, MOI.DualStatus(), MOI.FeasiblePoint)
     MOI.set(mock, MOI.ResultCount(), 1)
@@ -120,31 +120,28 @@ to a setting such as a time limit. We can ask the solver why it stopped using
 the `JuMP.termination_status` function:
 ```jldoctest quickstart_example
 julia> JuMP.termination_status(model)
-Success::TerminationStatusCode = 1
+Optimal::TerminationStatusCode = 1
 ```
-In this case, `GLPK` returned `Success`. This does *not* mean that it has found
-the optimal solution. Instead, it indicates that GLPK has finished running and
-did not encounter any errors or user-provided termination limits.
+In this case, `GLPK` returned `Optimal`, this mean that it has found the optimal
+solution.
 
 ```@meta
 DocTestSetup = nothing
 ```
 
-To understand the reason for termination in more detail, we need to query
-`JuMP.primalstatus`:
+As the solver found an optimal solution, we expect the solution returned to be
+a primal-dual pair of feasible solutions with zero duality gap.
+We can verify the primal and dual status as follows to confirm this:
 ```jldoctest quickstart_example
 julia> JuMP.primal_status(model)
 FeasiblePoint::ResultStatusCode = 1
-```
-This indicates that GLPK has found a `FeasiblePoint` to the primal problem.
-Coupled with the `Success` from `JuMP.termination_status`, we can infer that GLPK
-has indeed found the optimal solution. We can also query `JuMP.dual_status`:
-```jldoctest quickstart_example
+
 julia> JuMP.dual_status(model)
 FeasiblePoint::ResultStatusCode = 1
 ```
-Like the `primal_status`, GLPK indicates that it has found a `FeasiblePoint` to
-the dual problem.
+Note that the primal and dual status only inform that the primal and dual
+solutions are feasible and it is only because we verified that the termination
+status is `Optimal` that we can conclude that they form an optimal solution.
 
 Finally, we can query the result of the optimization. First, we can query the
 objective value:
diff --git a/examples/cannery.jl b/examples/cannery.jl
index c6dbb40c583..3091bdd1637 100644
--- a/examples/cannery.jl
+++ b/examples/cannery.jl
@@ -53,7 +53,7 @@ function solveCannery(plants, markets, capacity, demand, distance, freight)
 
   term_status = JuMP.termination_status(cannery)
   primal_status = JuMP.primal_status(cannery)
-  is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+  is_optimal = term_status == MOI.Optimal
 
   PrintSolution(is_optimal, plants, markets, ship)
   return is_optimal
diff --git a/examples/diet.jl b/examples/diet.jl
index f4ee81c0706..e35af475442 100644
--- a/examples/diet.jl
+++ b/examples/diet.jl
@@ -74,7 +74,7 @@ function SolveDiet()
     JuMP.optimize!(m)
     term_status = JuMP.termination_status(m)
     primal_status = JuMP.primal_status(m)
-    is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+    is_optimal = term_status == MOI.Optimal
 
     PrintSolution(is_optimal, foods, buy)
 
@@ -85,7 +85,7 @@ function SolveDiet()
     JuMP.optimize!(m)
     term_status = JuMP.termination_status(m)
     primal_status = JuMP.primal_status(m)
-    is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+    is_optimal = term_status == MOI.Optimal
 
     PrintSolution(is_optimal, foods, buy)
 end
diff --git a/examples/multi.jl b/examples/multi.jl
index ee15ffeb592..7de4fea9d03 100644
--- a/examples/multi.jl
+++ b/examples/multi.jl
@@ -105,6 +105,6 @@ JuMP.optimize!(multi)
 
 term_status = JuMP.termination_status(multi)
 primal_status = JuMP.primal_status(multi)
-is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+is_optimal = term_status == MOI.Optimal
 
 PrintSolution(is_optimal, Trans, orig, dest, prod)
diff --git a/examples/prod.jl b/examples/prod.jl
index 4d73818120e..31df1f44025 100644
--- a/examples/prod.jl
+++ b/examples/prod.jl
@@ -253,6 +253,6 @@ JuMP.optimize!(prod)
 
 term_status = JuMP.termination_status(prod)
 primal_status = JuMP.primal_status(prod)
-is_optimal = status == MOI.Success && primal_status == MOI.FeasiblePoint
+is_optimal = status == MOI.Optimal
 
 PrintSolution(is_optimal, Crews, Hire, Layoff)
diff --git a/examples/steelT3.jl b/examples/steelT3.jl
index 3002241cc95..eb61c418226 100644
--- a/examples/steelT3.jl
+++ b/examples/steelT3.jl
@@ -123,6 +123,6 @@ JuMP.optimize!(Prod)
 
 term_status = JuMP.termination_status(Prod)
 primal_status = JuMP.primal_status(Prod)
-is_optimal = status == MOI.Success && primal_status == MOI.FeasiblePoint
+is_optimal = status == MOI.Optimal
 
 PrintSolution(is_optimal, area, Make, Inv, Sell, prod, T)
diff --git a/examples/sudoku.jl b/examples/sudoku.jl
index 93646a4eba1..99a4dea755e 100644
--- a/examples/sudoku.jl
+++ b/examples/sudoku.jl
@@ -65,7 +65,7 @@ function SolveModel(initgrid)
 
     term_status = JuMP.termination_status(m)
     primal_status = JuMP.primal_status(m)
-    is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+    is_optimal = term_status == MOI.Optimal
 
     # Check solution
     if is_optimal
diff --git a/examples/transp.jl b/examples/transp.jl
index 00e48d71ac3..13fb3888015 100644
--- a/examples/transp.jl
+++ b/examples/transp.jl
@@ -48,7 +48,7 @@ JuMP.optimize!(m)
 
 term_status = JuMP.termination_status(m)
 primal_status = JuMP.primal_status(m)
-is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+is_optimal = term_status == MOI.Optimal
 
 if is_optimal
 	@printf("Optimal!\n")
diff --git a/examples/urbanplan.jl b/examples/urbanplan.jl
index ce3221ef7ca..9058ba5733c 100644
--- a/examples/urbanplan.jl
+++ b/examples/urbanplan.jl
@@ -70,7 +70,7 @@ function SolveUrban()
 
     term_status = JuMP.termination_status(m)
     primal_status = JuMP.primal_status(m)
-    is_optimal = term_status == MOI.Success && primal_status == MOI.FeasiblePoint
+    is_optimal = term_status == MOI.Optimal
 
     if ! is_optimal
         error("The solver did not find an optimal solution.")
diff --git a/test/constraint.jl b/test/constraint.jl
index 9fbda0a2f3c..e67d98fa27d 100644
--- a/test/constraint.jl
+++ b/test/constraint.jl
@@ -339,7 +339,7 @@ function test_shadow_price(model_string, constraint_dual, constraint_shadow)
                                          eval_objective_value=false,
                                          eval_variable_constraint_dual=false))
     mock_optimizer = JuMP.backend(model).optimizer.model
-    MOI.set(mock_optimizer, MOI.TerminationStatus(), MOI.Success)
+    MOI.set(mock_optimizer, MOI.TerminationStatus(), MOI.Optimal)
     MOI.set(mock_optimizer, MOI.DualStatus(), MOI.FeasiblePoint)
     JuMP.optimize!(model)
 
diff --git a/test/generate_and_solve.jl b/test/generate_and_solve.jl
index af1896e02d6..23d42c703b5 100644
--- a/test/generate_and_solve.jl
+++ b/test/generate_and_solve.jl
@@ -44,7 +44,7 @@
                                          eval_objective_value=false))
 
         mockoptimizer = JuMP.backend(m).optimizer.model
-        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Success)
+        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Optimal)
         MOI.set(mockoptimizer, MOI.ObjectiveValue(), -1.0)
         MOI.set(mockoptimizer, MOI.ResultCount(), 1)
         MOI.set(mockoptimizer, MOI.PrimalStatus(), MOI.FeasiblePoint)
@@ -58,7 +58,7 @@
         #@test JuMP.isattached(m)
         @test JuMP.has_values(m)
 
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.Optimal
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value(x) == 1.0
@@ -82,7 +82,7 @@
         @objective(m, Min, -x)
 
         c = @constraint(m, x + y <= 1)
-        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Success)
+        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Optimal)
         MOI.set(mockoptimizer, MOI.ObjectiveValue(), -1.0)
         MOI.set(mockoptimizer, MOI.ResultCount(), 1)
         MOI.set(mockoptimizer, MOI.PrimalStatus(), MOI.FeasiblePoint)
@@ -98,7 +98,7 @@
         #@test JuMP.isattached(m)
         @test JuMP.has_values(m)
 
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.Optimal
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value(x) == 1.0
@@ -143,7 +143,7 @@
         MOIU.attachoptimizer!(m)
 
         mockoptimizer = JuMP.backend(m).optimizer.model
-        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Success)
+        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Optimal)
         MOI.set(mockoptimizer, MOI.ObjectiveValue(), 1.0)
         MOI.set(mockoptimizer, MOI.ResultCount(), 1)
         MOI.set(mockoptimizer, MOI.PrimalStatus(), MOI.FeasiblePoint)
@@ -156,7 +156,7 @@
         #@test JuMP.isattached(m)
         @test JuMP.has_values(m)
 
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.Optimal
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value(x) == 1.0
@@ -193,7 +193,7 @@
                                          eval_objective_value=false))
 
         mockoptimizer = JuMP.backend(m).optimizer.model
-        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Success)
+        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Optimal)
         MOI.set(mockoptimizer, MOI.ObjectiveValue(), -1.0)
         MOI.set(mockoptimizer, MOI.ResultCount(), 1)
         MOI.set(mockoptimizer, MOI.PrimalStatus(), MOI.FeasiblePoint)
@@ -207,7 +207,7 @@
         #@test JuMP.isattached(m)
         @test JuMP.has_values(m)
 
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.Optimal
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value(x) == 1.0
@@ -253,7 +253,7 @@
         MOIU.resetoptimizer!(m, mockoptimizer)
         MOIU.attachoptimizer!(m)
 
-        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Success)
+        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Optimal)
         MOI.set(mockoptimizer, MOI.ResultCount(), 1)
         MOI.set(mockoptimizer, MOI.PrimalStatus(), MOI.FeasiblePoint)
         MOI.set(mockoptimizer, MOI.DualStatus(), MOI.FeasiblePoint)
@@ -268,7 +268,7 @@
         #@test JuMP.isattached(m)
         @test JuMP.has_values(m)
 
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.Optimal
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value(x) == 1.0
@@ -314,7 +314,7 @@
         MOIU.resetoptimizer!(m, mockoptimizer)
         MOIU.attachoptimizer!(m)
 
-        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Success)
+        MOI.set(mockoptimizer, MOI.TerminationStatus(), MOI.Optimal)
         MOI.set(mockoptimizer, MOI.ResultCount(), 1)
         MOI.set(mockoptimizer, MOI.PrimalStatus(), MOI.FeasiblePoint)
         MOI.set(mockoptimizer, MOI.DualStatus(), MOI.FeasiblePoint)
@@ -330,7 +330,7 @@
 
         JuMP.optimize!(m)
 
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.Optimal
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.has_values(m)
diff --git a/test/nlp_solver.jl b/test/nlp_solver.jl
index 8bc2acfcbab..8b880568fd8 100644
--- a/test/nlp_solver.jl
+++ b/test/nlp_solver.jl
@@ -47,7 +47,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value.(x) ≈ [1.000000, 4.742999, 3.821150, 1.379408] atol=1e-3
@@ -78,7 +78,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value.(x) ≈ [1.000000, 4.742999, 3.821150, 1.379408] atol=1e-3
@@ -126,7 +126,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.objective_value(m) ≈ 5326.851310161077 atol=1e-5
@@ -144,8 +144,8 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        # Ipopt returns AlmostSuccess and NearlyFeasiblePoint on this instance.
-        # @test JuMP.termination_status(m) == MOI.Success
+        # Ipopt returns AlmostLocallySolved and NearlyFeasiblePoint on this instance.
+        # @test JuMP.termination_status(m) == MOI.LocallySolved
         # @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.objective_value(m) ≈ -45.77846971 atol=1e-5
@@ -167,7 +167,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.objective_value(m) ≈ -47.76109026 atol=1e-5
@@ -188,7 +188,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.objective_value(m) ≈ -47.76109026 atol=1e-5
@@ -223,7 +223,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.objective_value(m) ≈ -1768.80696 atol=1e-3
@@ -269,7 +269,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         # This test occasionally fails, for unknown reasons.
@@ -337,7 +337,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
         @test JuMP.value.(x[1:4]) ≈ [8.0, 49.0, 3.0, 1.0] atol=1e-4
@@ -354,7 +354,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ u atol=1e-6
 
@@ -362,7 +362,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ l atol=1e-6
     end
@@ -377,7 +377,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ u atol=1e-6
 
@@ -385,7 +385,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ l atol=1e-6
     end
@@ -403,7 +403,7 @@ const MOI = MathOptInterface
 
         function test_result()
             @test JuMP.has_values(m)
-            @test JuMP.termination_status(m) == MOI.Success
+            @test JuMP.termination_status(m) == MOI.LocallySolved
             @test JuMP.primal_status(m) == MOI.FeasiblePoint
 
 
@@ -455,7 +455,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ -1-4/sqrt(3) atol=1e-6
         @test JuMP.value(x) + JuMP.value(y) ≈ -1/3 atol=1e-3
@@ -470,7 +470,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ -1-4/sqrt(3) atol=1e-6
         @test JuMP.value(x) + JuMP.value(y) ≈ -1/3 atol=1e-3
@@ -484,7 +484,7 @@ const MOI = MathOptInterface
         JuMP.optimize!(m)
 
         @test JuMP.has_values(m)
-        @test JuMP.termination_status(m) == MOI.Success
+        @test JuMP.termination_status(m) == MOI.LocallySolved
         @test JuMP.primal_status(m) == MOI.FeasiblePoint
         @test JuMP.objective_value(m) ≈ sqrt(1/2) atol=1e-6
         @test JuMP.value.(x) ≈ [sqrt(1/2), 0] atol=1e-6