Problem scema changes.

Added method that figures out if a problem is convex or not (by checking
the properteis of its function expressions).

desdeo/problem/schema.py

@@ -751,6 +751,26 @@ def variable_domain(self) -> VariableDomainTypeEnum:
         # mixed problem
         return VariableDomainTypeEnum.mixed
 
+    def is_convex(self) -> bool:
+        """Check if all the functions expressions in the problem are convex.
+
+        Note:
+            This method just checks all the functions expressions present in the problem
+            and return true if all of them are convex. For complicated problems, this might
+            result in an incorrect results. User discretion is advised.
+
+        Returns:
+            bool: whether the problem is convex or not.
+        """
+        is_convex_values = (
+            [obj.is_convex for obj in self.objectives]
+            + ([con.is_convex for con in self.constraints] if self.constraints is not None else [])
+            + ([extra.is_convex for extra in self.extra_funcs] if self.extra_funcs is not None else [])
+            + ([scal.is_convex for scal in self.scalarization_funcs] if self.scalarization_funcs is not None else [])
+        )
+
+        return all(is_convex_values)
+
     name: str = Field(
         description="Name of the problem.",
     )

desdeo/problem/testproblems.py

@@ -90,12 +90,25 @@ def binh_and_korn(maximize: tuple[bool] = (False, False)) -> Problem:
 
 
 def river_pollution_problem(five_objective_variant: bool = True) -> Problem:
-    """Create a pydantic dataclass representation of the river pollution problem with either five or four variables.
+    r"""Create a pydantic dataclass representation of the river pollution problem with either five or four variables.
 
     The objective functions "DO city", "DO municipality", and
     "BOD deviation" are to be minimized, while "ROI fishery" and "ROI city" are to be
     maximized. If the four variant problem is used, the the "BOD deviation" objective
-    function is not present.
+    function is not present. The problem is defined as follows:
+
+    \begin{align*}
+    \min f_1(x) &= -4.07 - 2.27 x_1 \\
+    \min f_2(x) &= -2.60 - 0.03 x_1 - 0.02 x_2 - \frac{0.01}{1.39 - x_1^2} - \frac{0.30}{1.39 - x_2^2} \\
+    \max f_3(x) &= 8.21 - \frac{0.71}{1.09 - x_1^2} \\
+    \max f_4(x) &= 0.96 - \frac{0.96}{1.09 - x_2^2} \\
+    \min f_5(x) &= \max(|x_1 - 0.65|, |x_2 - 0.65|) \\
+    \text{s.t.}\quad    & 0.3 \leq x_1 \leq 1.0,\\
+                        & 0.3 \leq x_2 \leq 1.0,\\
+    \end{align*}
+
+    where the fifth objective is part of the problem definition only if
+    `five_objective_variant = True`.
 
     Args:
         five_objective_variant (bool, optional): Whether to use to five
@@ -111,7 +124,7 @@ def river_pollution_problem(five_objective_variant: bool = True) -> Problem:
 
         Miettinen, Kaisa, and Marko M. Mäkelä. "Interactive method NIMBUS for
             nondifferentiable multiobjective optimization problems." Multicriteria
-            Analysis: Proceedings of the XIth International Conference on MCDM, 1–6
+            Analysis: Proceedings of the XIth International Conference on MCDM, 1-6
             August 1994, Coimbra, Portugal. Berlin, Heidelberg: Springer Berlin
             Heidelberg, 1997.
     """
@@ -128,11 +141,61 @@ def river_pollution_problem(five_objective_variant: bool = True) -> Problem:
     f_4 = "0.96 - 0.96 / (1.09 - x_2**2)"
     f_5 = "Max(Abs(x_1 - 0.65), Abs(x_2 - 0.65))"
 
-    objective_1 = Objective(name="DO city", symbol="f_1", func=f_1, maximize=False, ideal=-6.34, nadir=-4.75)
-    objective_2 = Objective(name="DO municipality", symbol="f_2", func=f_2, maximize=False, ideal=-3.44, nadir=-2.85)
-    objective_3 = Objective(name="ROI fishery", symbol="f_3", func=f_3, maximize=True, ideal=7.5, nadir=0.32)
-    objective_4 = Objective(name="ROI city", symbol="f_4", func=f_4, maximize=True, ideal=0, nadir=-9.70)
-    objective_5 = Objective(name="BOD deviation", symbol="f_5", func=f_5, maximize=False, ideal=0, nadir=0.35)
+    objective_1 = Objective(
+        name="DO city",
+        symbol="f_1",
+        func=f_1,
+        maximize=False,
+        ideal=-6.34,
+        nadir=-4.75,
+        is_convex=True,
+        is_linear=True,
+        is_twice_differentiable=True,
+    )
+    objective_2 = Objective(
+        name="DO municipality",
+        symbol="f_2",
+        func=f_2,
+        maximize=False,
+        ideal=-3.44,
+        nadir=-2.85,
+        is_convex=False,
+        is_linear=False,
+        is_twice_differentiable=True,
+    )
+    objective_3 = Objective(
+        name="ROI fishery",
+        symbol="f_3",
+        func=f_3,
+        maximize=True,
+        ideal=7.5,
+        nadir=0.32,
+        is_convex=True,
+        is_linear=False,
+        is_twice_differentiable=True,
+    )
+    objective_4 = Objective(
+        name="ROI city",
+        symbol="f_4",
+        func=f_4,
+        maximize=True,
+        ideal=0,
+        nadir=-9.70,
+        is_convex=True,
+        is_linear=False,
+        is_twice_differentiable=True,
+    )
+    objective_5 = Objective(
+        name="BOD deviation",
+        symbol="f_5",
+        func=f_5,
+        maximize=False,
+        ideal=0,
+        nadir=0.35,
+        is_convex=False,
+        is_linear=False,
+        is_twice_differentiable=False,
+    )
 
     objectives = (
         [objective_1, objective_2, objective_3, objective_4, objective_5]

tests/test_problem_schema.py

@@ -491,3 +491,14 @@ def test_variable_domain():
     integer_problem = simple_knapsack()
 
     assert integer_problem.variable_domain() == VariableDomainTypeEnum.integer
+
+
+def test_is_convex():
+    """Test whether the convexity of a problem is inferred correctly."""
+    problem_convex = simple_knapsack()
+
+    assert problem_convex.is_convex()
+
+    problem_non_convex = river_pollution_problem()
+
+    assert not problem_non_convex.is_convex()