diff --git a/src/pyvmcon/problem.py b/src/pyvmcon/problem.py
index bb3f305..e42c771 100644
--- a/src/pyvmcon/problem.py
+++ b/src/pyvmcon/problem.py
@@ -2,19 +2,22 @@
 
 from abc import ABC, abstractmethod
 from collections.abc import Callable
-from typing import NamedTuple, TypeVar
+from dataclasses import dataclass, field
+from typing import TypeVar, cast
 
 import numpy as np
+from numpy.typing import NDArray
 
-ScalarType = TypeVar("ScalarType", np.ndarray, np.number, float)
+ScalarType = TypeVar("ScalarType", NDArray, np.number, float)
 """A scalar variable e.g. a single number (which could be a 0D numpy array)"""
-VectorType = TypeVar("VectorType", bound=np.ndarray)
+VectorType = NDArray
 """A numpy array with only 1 dimension"""
-MatrixType = TypeVar("MatrixType", bound=np.ndarray)
+MatrixType = NDArray
 """A numpy array with 2 dimensions"""
 
 
-class Result(NamedTuple):
+@dataclass
+class Result:
     """The data from calling a problem."""
 
     f: ScalarType
@@ -80,6 +83,7 @@ def total_constraints(self) -> int:
 _VectorReturnFunctionAlias = Callable[[VectorType], VectorType]
 
 
+@dataclass
 class Problem(AbstractProblem):
     """A simple implementation of an AbstractProblem.
 
@@ -89,42 +93,36 @@ class Problem(AbstractProblem):
     feasible when they return a value >= 0.
     """
 
-    def __init__(
-        self,
-        f: _ScalarReturnFunctionAlias,
-        df: _VectorReturnFunctionAlias,
-        equality_constraints: list[_ScalarReturnFunctionAlias] | None = None,
-        inequality_constraints: list[_ScalarReturnFunctionAlias] | None = None,
-        dequality_constraints: list[_VectorReturnFunctionAlias] | None = None,
-        dinequality_constraints: list[_VectorReturnFunctionAlias] | None = None,
-    ) -> None:
-        """Construct the problem."""
-        super().__init__()
-
-        self._f = f
-        self._df = df
-        self._equality_constraints = equality_constraints or []
-        self._inequality_constraints = inequality_constraints or []
-        self._dequality_constraints = dequality_constraints or []
-        self._dinequality_constraints = dinequality_constraints or []
+    f: _ScalarReturnFunctionAlias
+    df: _VectorReturnFunctionAlias
+    equality_constraints: list[_ScalarReturnFunctionAlias] = field(default_factory=list)
+    inequality_constraints: list[_ScalarReturnFunctionAlias] = field(
+        default_factory=list
+    )
+    dequality_constraints: list[_VectorReturnFunctionAlias] = field(
+        default_factory=list
+    )
+    dinequality_constraints: list[_VectorReturnFunctionAlias] = field(
+        default_factory=list
+    )
 
     def __call__(self, x: VectorType) -> Result:
         """Evaluate the problem at input point x."""
         return Result(
-            self._f(x),
-            self._df(x),
-            np.array([c(x) for c in self._equality_constraints]),
-            np.array([c(x) for c in self._dequality_constraints]),
-            np.array([c(x) for c in self._inequality_constraints]),
-            np.array([c(x) for c in self._dinequality_constraints]),
+            self.f(x),
+            self.df(x),
+            cast("VectorType", np.array([c(x) for c in self.equality_constraints])),
+            cast("MatrixType", np.array([c(x) for c in self.dequality_constraints])),
+            cast("VectorType", np.array([c(x) for c in self.inequality_constraints])),
+            cast("MatrixType", np.array([c(x) for c in self.dinequality_constraints])),
         )
 
     @property
     def num_equality(self) -> int:
         """The number of equality constraints this problem has."""
-        return len(self._equality_constraints)
+        return len(self.equality_constraints)
 
     @property
     def num_inequality(self) -> int:
         """The number of inequality constraints this problem has."""
-        return len(self._inequality_constraints)
+        return len(self.inequality_constraints)
diff --git a/src/pyvmcon/vmcon.py b/src/pyvmcon/vmcon.py
index ef69352..3dce4dd 100644
--- a/src/pyvmcon/vmcon.py
+++ b/src/pyvmcon/vmcon.py
@@ -2,18 +2,19 @@
 
 import logging
 from collections.abc import Callable
-from typing import Any
+from typing import Any, cast
 
 import cvxpy as cp
 import numpy as np
 
+from pyvmcon.problem import AbstractProblem, MatrixType, Result, ScalarType, VectorType
+
 from .exceptions import (
     LineSearchConvergenceException,
     QSPSolverException,
     VMCONConvergenceException,
     _QspSolveException,
 )
-from .problem import AbstractProblem, MatrixType, Result, ScalarType, VectorType
 
 logger = logging.getLogger(__name__)
 
@@ -439,8 +440,10 @@ def perform_linesearch(
     mu_inequality = _calculate_mu_j(mu_inequality, lamda_inequality)
 
     def phi(result: Result) -> ScalarType:
-        sum_equality = (mu_equality * np.abs(result.eq)).sum()
-        sum_inequality = (mu_inequality * np.abs(np.minimum(0, result.ie))).sum()
+        sum_equality: ScalarType = (mu_equality * np.abs(result.eq)).sum()
+        sum_inequality: ScalarType = (
+            mu_inequality * np.abs(np.minimum(0, result.ie))
+        ).sum()
 
         return result.f + sum_equality + sum_inequality
 
@@ -476,7 +479,7 @@ def phi(result: Result) -> ScalarType:
             lamda_inequality=lamda_inequality,
         )
 
-    return alpha, mu_equality, mu_inequality, new_result
+    return cast("ScalarType", alpha), mu_equality, mu_inequality, new_result
 
 
 def _derivative_lagrangian(