diff --git a/cpp/src/linear_programming/solve.cu b/cpp/src/linear_programming/solve.cu
index ed2a30bcf..c3ba4f2c7 100644
--- a/cpp/src/linear_programming/solve.cu
+++ b/cpp/src/linear_programming/solve.cu
@@ -346,16 +346,30 @@ optimization_problem_solution_t<i_t, f_t> run_dual_simplex(
                                   std::get<4>(sol_dual_simplex));
 }
 
+template <typename i_t, typename f_t>
+static optimization_problem_solution_t<i_t, f_t> run_pdlp_solver(
+  detail::problem_t<i_t, f_t>& problem,
+  pdlp_solver_settings_t<i_t, f_t> const& settings,
+  const std::chrono::high_resolution_clock::time_point& start_time)
+{
+  if (problem.n_constraints == 0) {
+    CUOPT_LOG_INFO("No constraints in the problem: PDLP can't be run, use Dual Simplex instead.");
+    return optimization_problem_solution_t<i_t, f_t>{pdlp_termination_status_t::NumericalError,
+                                                     problem.handle_ptr->get_stream()};
+  }
+  detail::pdlp_solver_t<i_t, f_t> solver(problem, settings);
+  return solver.run_solver(start_time);
+}
+
 template <typename i_t, typename f_t>
 optimization_problem_solution_t<i_t, f_t> run_pdlp(detail::problem_t<i_t, f_t>& problem,
                                                    pdlp_solver_settings_t<i_t, f_t> const& settings)
 {
   auto start_solver = std::chrono::high_resolution_clock::now();
   f_t start_time    = dual_simplex::tic();
-  detail::pdlp_solver_t<i_t, f_t> solver(problem, settings);
-  auto sol      = solver.run_solver(start_solver);  // Passing it for time limit
-  auto end      = std::chrono::high_resolution_clock::now();
-  auto duration = std::chrono::duration_cast<std::chrono::milliseconds>(end - start_solver);
+  auto sol          = run_pdlp_solver(problem, settings, start_solver);
+  auto end          = std::chrono::high_resolution_clock::now();
+  auto duration     = std::chrono::duration_cast<std::chrono::milliseconds>(end - start_solver);
   sol.set_solve_time(duration.count() / 1000.0);
   CUOPT_LOG_INFO("PDLP finished");
   if (sol.get_termination_status() != pdlp_termination_status_t::ConcurrentLimit) {
diff --git a/cpp/src/mip/problem/problem.cu b/cpp/src/mip/problem/problem.cu
index 5b8511b92..e036696de 100644
--- a/cpp/src/mip/problem/problem.cu
+++ b/cpp/src/mip/problem/problem.cu
@@ -53,23 +53,7 @@ template <typename i_t, typename f_t>
 void problem_t<i_t, f_t>::op_problem_cstr_body(const optimization_problem_t<i_t, f_t>& problem_)
 {
   // Mark the problem as empty if the op_problem has an empty matrix.
-  if (problem_.get_constraint_matrix_values().is_empty()) {
-    cuopt_assert(problem_.get_constraint_matrix_indices().is_empty(),
-                 "Problem is empty but constraint matrix indices are not empty.");
-    cuopt_assert(problem_.get_constraint_matrix_offsets().size() == 1,
-                 "Problem is empty but constraint matrix offsets are not empty.");
-    cuopt_assert(problem_.get_objective_coefficients().is_empty(),
-                 "Problem is empty but objective coefficients are not empty.");
-    cuopt_assert(problem_.get_variable_lower_bounds().is_empty(),
-                 "Problem is empty but variable lower bounds are not empty.");
-    cuopt_assert(problem_.get_variable_upper_bounds().is_empty(),
-                 "Problem is empty but variable upper bounds are not empty.");
-    cuopt_assert(problem_.get_constraint_lower_bounds().is_empty(),
-                 "Problem is empty but constraint lower bounds are not empty.");
-    cuopt_assert(problem_.get_constraint_upper_bounds().is_empty(),
-                 "Problem is empty but constraint upper bounds are not empty.");
-    empty = true;
-  }
+  if (problem_.get_constraint_matrix_values().is_empty()) { empty = true; }
 
   // Set variables bounds to default if not set and constraints bounds if user has set a row type
   set_bounds_if_not_set(*this);
diff --git a/cpp/tests/linear_programming/pdlp_test.cu b/cpp/tests/linear_programming/pdlp_test.cu
index 64908261c..212e4e1d3 100644
--- a/cpp/tests/linear_programming/pdlp_test.cu
+++ b/cpp/tests/linear_programming/pdlp_test.cu
@@ -871,6 +871,41 @@ TEST(dual_simplex, afiro)
     afiro_primal_objective, solution.get_additional_termination_information().primal_objective));
 }
 
+// Should return a numerical error
+TEST(pdlp_class, run_empty_matrix_pdlp)
+{
+  const raft::handle_t handle_{};
+
+  auto path = make_path_absolute("linear_programming/empty_matrix.mps");
+  cuopt::mps_parser::mps_data_model_t<int, double> op_problem =
+    cuopt::mps_parser::parse_mps<int, double>(path);
+
+  auto solver_settings   = pdlp_solver_settings_t<int, double>{};
+  solver_settings.method = cuopt::linear_programming::method_t::PDLP;
+
+  optimization_problem_solution_t<int, double> solution =
+    solve_lp(&handle_, op_problem, solver_settings);
+  EXPECT_EQ((int)solution.get_termination_status(), CUOPT_TERIMINATION_STATUS_NUMERICAL_ERROR);
+}
+
+// Should run thanks to Dual Simplex
+TEST(pdlp_class, run_empty_matrix_dual_simplex)
+{
+  const raft::handle_t handle_{};
+
+  auto path = make_path_absolute("linear_programming/empty_matrix.mps");
+  cuopt::mps_parser::mps_data_model_t<int, double> op_problem =
+    cuopt::mps_parser::parse_mps<int, double>(path);
+
+  auto solver_settings   = pdlp_solver_settings_t<int, double>{};
+  solver_settings.method = cuopt::linear_programming::method_t::Concurrent;
+
+  optimization_problem_solution_t<int, double> solution =
+    solve_lp(&handle_, op_problem, solver_settings);
+  EXPECT_EQ((int)solution.get_termination_status(), CUOPT_TERIMINATION_STATUS_OPTIMAL);
+  EXPECT_FALSE(solution.get_additional_termination_information().solved_by_pdlp);
+}
+
 }  // namespace cuopt::linear_programming::test
 
 CUOPT_TEST_PROGRAM_MAIN()
diff --git a/datasets/linear_programming/empty_matrix.mps b/datasets/linear_programming/empty_matrix.mps
new file mode 100644
index 000000000..e387ee780
--- /dev/null
+++ b/datasets/linear_programming/empty_matrix.mps
@@ -0,0 +1,11 @@
+NAME
+ROWS
+  N  OBJ
+COLUMNS
+     x1        OBJ       -3
+RHS
+RANGES
+BOUNDS
+  MI bounds    x1
+  UP bounds    x1        2
+ENDATA