[ready for review] better handling of all infeasible/unbounded in best of

cvxpy/reductions/solvers/nlp_solving_chain.py

@@ -209,12 +209,17 @@ def solve_nlp(problem, solver, warm_start, verbose, **kwargs):
                                                    verbose, solver_opts=kwargs,
                                                    solver_cache=solver_cache)
 
-        # Unpack to get the objective value in the original problem space
+        # unpack to get the objective value in the original problem space.
+        # (+inf for infeasible runs, -inf for unbounded runs)
         problem.unpack_results(solution, nlp_chain, inverse_data)
-        obj_value = problem.objective.value
+        obj_value = problem.value
 
         all_objs[run] = obj_value
-        if obj_value is not None and obj_value < best_obj:
+
+        # always set best_solution with the first run so that even an
+        # all-infeasible best_of has a solution to unpack at the end (its
+        # INFEASIBLE status then propagates through unpack_results).
+        if best_solution is None or obj_value < best_obj:
             best_obj = obj_value
             best_solution = solution
 

cvxpy/tests/nlp_tests/test_best_of.py

@@ -114,4 +114,21 @@ def test_path_planning_best_of_five(self):
         all_objs = prob.solver_stats.extra_stats['all_objs_from_best_of']
         assert len(all_objs) == 3
 
-# TODO add a test that best_of actually caches the sparsity pattern between solves
+    def test_best_of_infeasible_problem(self):
+        # test that if the problem is infeasible, then best_of returns inf as the objective value
+        x = cp.Variable(bounds=[-5, 5])
+        y = cp.Variable(bounds=[-3, 3])
+        constraints = [x + y == 10]
+        obj = cp.Minimize((x - 1) ** 2 + (y - 2) ** 2)
+        prob = cp.Problem(obj, constraints)
+        prob.solve(nlp=True, best_of=20, verbose=True)
+        assert prob.value == float("inf")
+
+    def test_best_of_with_unbounded(self):
+        # test that if the problem is unbounded, then best_of returns -inf as the objective value
+        x = cp.Variable()
+        x.sample_bounds = [-5, 5]
+        obj = cp.Minimize(x)
+        prob = cp.Problem(obj)
+        prob.solve(nlp=True, best_of=20, verbose=True)
+        assert prob.value == float("-inf")