Make solver_path fall back on non-optimal statuses (cvxpy#3324)

* Make solver_path reject non-optimal statuses

* Address solver_path review feedback

Author: curious7-web

cvxpy/problems/problem.py

@@ -575,7 +575,14 @@ def _solve_solver_path(self, solve_func, solvers:list[tuple[str, dict] | str],
                             self, *args, solver=solver_name, **solver_kwargs, **kwargs)
                 else:
                     raise ValueError(ENTRY_ERROR_MSG)
-                s.LOGGER.info("Solver %s succeeds", solver_name)
+                if self.status == s.OPTIMAL:
+                    s.LOGGER.info("Solver %s succeeds", solver_name)
+                else:
+                    s.LOGGER.info("Solver %s returned non-optimal status %s",
+                                  solver_name,
+                                  self.status
+                                  )
+                    continue
                 return solution
             except error.SolverError as e:
                 s.LOGGER.info("Solver %s failed: %s", solver_name, e)

cvxpy/tests/test_problem.py

@@ -1542,15 +1542,18 @@ def test_solve_solver_path(self) -> None:
             self.assertIsNotNone(Problem(cp.Minimize(
                 cp.sum_squares(cp.matmul(A, cp.Variable(40)) - b))).solve(
                 solver_path=solvers))
-
+        # valid input, non-optimal first solver falls back to next solver
+        problem = Problem(cp.Minimize(
+            cp.sum_squares(cp.matmul(A, cp.Variable(40)) - b)))
+        problem.solve(solver_path=[(s.OSQP, {'max_iter': 1}), s.CLARABEL])
+        self.assertEqual(problem.solver_stats.solver_name, s.CLARABEL)
+        self.assertEqual(problem.status, s.OPTIMAL)
         # valid input, raise SolverError
         solvers = [(s.OSQP, {'max_iter':1})]
-
         with self.assertRaises(SolverError):
             Problem(cp.Minimize(cp.quad_form(cp.Variable(1) + 1, np.array([[-1]]), True))).solve(
                 solver_path=solvers
             )
-
         # invalid input, raise ValueError
         solvers_invalid_inner_input = [{'str':{}}, 'str', [], [1], [()], [(1)], [(1,{})],
                                         [(s.OSQP,[])], [(s.OSQP,)]]