diff --git a/test/test_lp.jl b/test/test_lp.jl
index f4699c694..c2a511fca 100644
--- a/test/test_lp.jl
+++ b/test/test_lp.jl
@@ -6,6 +6,10 @@
         solve!(p, solver)
         @test p.optval ≈ 1 atol=TOL
         @test evaluate(abs(x)) ≈ 1 atol=TOL
+        if p.solution.has_dual
+            println("Solution object has dual value, checking for dual correctness.")
+            @test p.constraints[1].dual ≈ 1 atol=TOL
+        end
 
         x = Variable(2,2)
         p = minimize(sum(abs(x)), x[2,2]>=1, x[1,1]>=1, x>=0)
@@ -13,6 +17,14 @@
         solve!(p, solver)
         @test p.optval ≈ 2 atol=TOL
         @test evaluate(sum(abs(x))) ≈ 2 atol=TOL
+        if p.solution.has_dual
+            println("Solution object has dual value, checking for dual correctness.")
+            @test p.constraints[1].dual ≈ 1 atol=TOL
+            @test p.constraints[2].dual ≈ 1 atol=TOL
+            @test p.constraints[3].dual[1,1] ≈ 0 atol=TOL
+            @test p.constraints[3].dual[2,2] ≈ 0 atol=TOL
+            @test p.constraints[3].dual[1,2] ≈ p.constraints[3].dual[2,1] atol=TOL
+        end
     end
 
     @testset "maximum atom" begin
@@ -155,6 +167,11 @@
         solve!(p, solver)
         @test p.optval ≈ 0 atol=TOL
         @test evaluate(norm_inf(x)) ≈ 0 atol=TOL
+        if p.solution.has_dual
+            println("Solution object has dual value, checking for dual correctness.")
+            @test norm(p.constraints[1].dual) ≈ 0 atol=TOL
+            @test norm(p.constraints[2].dual) ≈ 0 atol=TOL
+        end
     end
 
     @testset "norm 1 atom" begin
@@ -164,5 +181,10 @@
         solve!(p, solver)
         @test p.optval ≈ 0 atol=TOL
         @test evaluate(norm_1(x)) ≈ 0 atol=TOL
+        if p.solution.has_dual
+            println("Solution object has dual value, checking for dual correctness.")
+            @test norm(p.constraints[1].dual) ≈ 0 atol=TOL
+            @test norm(p.constraints[2].dual) ≈ 0 atol=TOL
+        end
     end
 end
diff --git a/test/test_socp.jl b/test/test_socp.jl
index 36e43a6ba..3ce701441 100644
--- a/test/test_socp.jl
+++ b/test/test_socp.jl
@@ -19,15 +19,23 @@
             solve!(p, solver)
             @test p.optval ≈ 14.9049 atol=TOL
             @test evaluate(norm2(A * x + b) + lambda * norm2(x)) ≈ 14.9049 atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual correctness.")
+                dual = [4.4134, 5.1546]
+                @test p.constraints[1].dual ≈ dual atol=TOL
+            end
 
             x = Variable(2)
-
             p = minimize(norm2([x[1] + 2x[2] + 2; 2x[1] + x[2] + 3; 3x[1]+4x[2] + 4]) + lambda * norm2(x), x >= 1)
             @test vexity(p) == ConvexVexity()
-
             solve!(p, solver)
             @test p.optval ≈ 14.9049 atol=TOL
             @test evaluate(norm2(A * x + b) + lambda * norm2(x)) ≈ 14.9049 atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual correctness.")
+                dual = [4.4134, 5.1546]
+                @test p.constraints[1].dual ≈ dual atol=TOL
+            end
 
             x = Variable(2, 1)
             A = [1 2; 2 1; 3 4]
@@ -38,6 +46,11 @@
             solve!(p, solver)
             @test p.optval ≈ 15.4907 atol=TOL
             @test evaluate(norm2(A * x + b) + lambda * norm_1(x)) ≈ 15.4907 atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual correctness.")
+                dual = [4.7062, 5.4475]
+                @test p.constraints[1].dual ≈ dual atol=TOL
+            end
         end
 
         @testset "frobenius norm atom" begin
@@ -48,6 +61,12 @@
             solve!(p, solver)
             @test p.optval ≈ sqrt(35) atol=TOL
             @test evaluate(norm(vec(m), 2)) ≈ sqrt(35) atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual correctness.")
+                @test p.constraints[1].dual ≈ 0.6761 atol=TOL
+                dual = 0.1690 .* ones(4, 5); dual[3, 3] = 0
+                @test p.constraints[2].dual ≈ dual atol=TOL
+            end
         end
 
         @testset "quad over lin atom" begin
@@ -277,5 +296,49 @@
                 @test o1 <= o2
             end
         end
+
+        @testset "minimal norm solutions" begin
+            x = Variable(2)
+            A = [1 2; 2 4];
+            b = [3, 6];
+            p = minimize(norm(x, 1), A*x==b)
+            @test vexity(p) == ConvexVexity()
+            solve!(p, solver)
+            @test p.optval ≈ 1.5 atol=TOL
+            @test evaluate(x) ≈ [0, 1.5] atol=TOL
+            @test evaluate(norm(x, 1)) ≈ p.optval atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual problem correctness.")
+                @test dot(b, p.constraints[1].dual) ≈ p.optval atol=TOL
+            end
+
+            x = Variable(2)
+            A = [1 2; 2 4];
+            b = [3, 6];
+            p = minimize(norm(x, 2), A*x==b)
+            @test vexity(p) == ConvexVexity()
+            solve!(p, solver)
+            @test p.optval ≈ 3/sqrt(5) atol=TOL
+            @test evaluate(x) ≈ [3/5, 6/5] atol=TOL
+            @test evaluate(norm(x, 2)) ≈ p.optval atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual problem correctness.")
+                @test dot(b, p.constraints[1].dual) ≈ p.optval atol=TOL
+            end
+
+            x = Variable(2)
+            A = [1 2; 2 4];
+            b = [3, 6];
+            p = minimize(norm(x, Inf), A*x==b)
+            @test vexity(p) == ConvexVexity()
+            solve!(p, solver)
+            @test p.optval ≈ 1.0 atol=TOL
+            @test evaluate(x) ≈ [1, 1] atol=TOL
+            @test evaluate(norm(x, Inf)) ≈ p.optval atol=TOL
+            if p.solution.has_dual
+                println("Solution object has dual value, checking for dual problem correctness.")
+                @test dot(b, p.constraints[1].dual) ≈ p.optval atol=TOL
+            end
+        end
     end
 end