diff --git a/pypesto/optimize/optimizer.py b/pypesto/optimize/optimizer.py
index 9b148acdc..26e712e4a 100644
--- a/pypesto/optimize/optimizer.py
+++ b/pypesto/optimize/optimizer.py
@@ -413,6 +413,36 @@ def set_maxeval(self, evaluations: int) -> None:
             f"Check supports_maxeval() before calling set_maxeval()."
         )
 
+    def supports_f_abs_tol(self) -> bool:
+        """
+        Check whether optimizer supports absolute function value tolerance.
+
+        Returns
+        -------
+        True if optimizer supports setting an absolute tolerance on the
+        objective function value, False otherwise.
+        """
+        return True
+
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance on function value for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance on objective function value for termination.
+
+        Raises
+        ------
+        NotImplementedError
+            If the optimizer does not support absolute function tolerance.
+        """
+        raise NotImplementedError(
+            f"{self.__class__.__name__} does not support absolute function tolerance. "
+            f"Check supports_f_abs_tol() before calling set_f_abs_tol()."
+        )
+
 
 class ScipyOptimizer(Optimizer):
     """
@@ -722,6 +752,24 @@ def set_maxtime(self, seconds: float) -> None:
 
         self._maxtime_seconds = seconds
 
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance on function value for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance on objective function value for termination.
+
+        Raises
+        ------
+        ValueError
+            If tolerance is negative.
+        """
+        if tol < 0:
+            raise ValueError(f"Tolerance must be non-negative, got {tol}")
+        self.tol = tol
+
 
 class IpoptOptimizer(Optimizer):
     """Use Ipopt (https://pypi.org/project/cyipopt/) for optimization."""
@@ -843,6 +891,10 @@ def set_maxiter(self, iterations: int) -> None:
             self.options = {}
         self.options["max_iter"] = iterations
 
+    def supports_f_abs_tol(self) -> bool:
+        """Check whether optimizer supports absolute function tolerance."""
+        return False
+
 
 class DlibOptimizer(Optimizer):
     """Use the Dlib toolbox for optimization."""
@@ -966,6 +1018,10 @@ def set_maxiter(self, iterations: int) -> None:
             self.options = {}
         self.options["maxiter"] = iterations
 
+    def supports_f_abs_tol(self) -> bool:
+        """Check whether optimizer supports absolute tolerance."""
+        return False
+
 
 class PyswarmOptimizer(Optimizer):
     """Global optimization using pyswarm."""
@@ -1041,6 +1097,26 @@ def set_maxiter(self, iterations: int) -> None:
             self.options = {}
         self.options["maxiter"] = iterations
 
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance for termination.
+
+        Raises
+        ------
+        ValueError
+            If tolerance is not positive.
+        """
+        if tol < 0:
+            raise ValueError(f"Tolerance must be positive, got {tol}")
+        if self.options is None:
+            self.options = {}
+        self.options["minfunc"] = tol
+
 
 class CmaOptimizer(Optimizer):
     """
@@ -1162,6 +1238,26 @@ def set_maxeval(self, evaluations: int) -> None:
             self.options = {}
         self.options["maxfevals"] = evaluations
 
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance for termination.
+
+        Raises
+        ------
+        ValueError
+            If tolerance is not positive.
+        """
+        if tol < 0:
+            raise ValueError(f"Tolerance must be positive, got {tol}")
+        if self.options is None:
+            self.options = {}
+        self.options["tolfun"] = tol
+
 
 class CmaesOptimizer(CmaOptimizer):
     """Deprecated, use CmaOptimizer instead."""
@@ -1263,6 +1359,26 @@ def set_maxiter(self, iterations: int) -> None:
             self.options = {}
         self.options["maxiter"] = iterations
 
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance for termination.
+
+        Raises
+        ------
+        ValueError
+            If tolerance is not positive.
+        """
+        if tol < 0:
+            raise ValueError(f"Tolerance must be positive, got {tol}")
+        if self.options is None:
+            self.options = {}
+        self.options["atol"] = tol
+
 
 class PyswarmsOptimizer(Optimizer):
     """
@@ -1404,6 +1520,10 @@ def set_maxiter(self, iterations: int) -> None:
             self.options = {}
         self.options["maxiter"] = iterations
 
+    def supports_f_abs_tol(self) -> bool:
+        """Check whether optimizer supports absolute tolerance."""
+        return False
+
 
 class NLoptOptimizer(Optimizer):
     """
@@ -1676,6 +1796,26 @@ def set_maxeval(self, evaluations: int) -> None:
         """
         self.options["maxeval"] = evaluations
 
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance for termination.
+
+        Raises
+        ------
+        ValueError
+            If tolerance is not positive.
+        """
+        if tol < 0:
+            raise ValueError(f"Tolerance must be positive, got {tol}")
+        if self.options is None:
+            self.options = {}
+        self.options["ftol_abs"] = tol
+
 
 class FidesOptimizer(Optimizer):
     """
@@ -1900,3 +2040,28 @@ def set_maxiter(self, iterations: int) -> None:
             self.options[FidesOptions.MAXITER] = iterations
         except ImportError:
             raise OptimizerImportError("fides") from None
+
+    def set_f_abs_tol(self, tol: float) -> None:
+        """
+        Set the absolute tolerance for optimization.
+
+        Parameters
+        ----------
+        tol
+            Absolute tolerance for termination.
+
+        Raises
+        ------
+        ValueError
+            If tolerance is not positive.
+        """
+        if tol < 0:
+            raise ValueError(f"Tolerance must be positive, got {tol}")
+        try:
+            from fides.constants import Options as FidesOptions
+
+            if self.options is None:
+                self.options = {}
+            self.options[FidesOptions.FATOL] = tol
+        except ImportError:
+            raise OptimizerImportError("fides") from None
diff --git a/test/optimize/test_optimizer_common_interface.py b/test/optimize/test_optimizer_common_interface.py
index bf39c8067..b2d3d4820 100644
--- a/test/optimize/test_optimizer_common_interface.py
+++ b/test/optimize/test_optimizer_common_interface.py
@@ -66,6 +66,15 @@ def test_ess_optimizer_support(self):
         optimizer.set_maxtime(10.0)
         assert optimizer.max_walltime_s == 10.0
 
+    def test_cma_optimizer_support(self):
+        """Test CmaOptimizer iteration limit support."""
+        optimizer = optimize.CmaOptimizer()
+
+        assert optimizer.supports_maxtime() is True
+        optimizer.set_maxtime(1000)
+
+        assert optimizer.options["timeout"] == 1000
+
     def test_scipy_optimizer_support(self):
         """Test ScipyOptimizer time limit support."""
         optimizer = optimize.ScipyOptimizer()
@@ -136,11 +145,6 @@ def test_cma_optimizer_support(self):
         optimizer.set_maxiter(5000)
         assert optimizer.options["maxiter"] == 5000
 
-        assert optimizer.supports_maxtime() is True
-        optimizer.set_maxtime(1000)
-
-        assert optimizer.options["timeout"] == 1000
-
     def test_scipy_de_optimizer_support(self):
         """Test ScipyDifferentialEvolutionOptimizer iteration limit support."""
         optimizer = optimize.ScipyDifferentialEvolutionOptimizer()
@@ -226,3 +230,99 @@ def test_ipopt_optimizer_no_support(self):
 
         with pytest.raises(NotImplementedError):
             optimizer.set_maxeval(100)
+
+
+class TestOptimizerTolInterface:
+    """Test the unified tolerance interface for optimizers."""
+
+    def test_scipy_optimizer_support(self):
+        """Test ScipyOptimizer tolerance support."""
+        optimizer = optimize.ScipyOptimizer()
+        assert optimizer.supports_f_abs_tol() is True
+
+        optimizer.set_f_abs_tol(1e-6)
+        assert optimizer.tol == 1e-6
+
+        # Test updating existing value
+        optimizer.set_f_abs_tol(1e-8)
+        assert optimizer.tol == 1e-8
+
+    def test_nlopt_optimizer_support(self):
+        """Test NLoptOptimizer tolerance support."""
+        optimizer = optimize.NLoptOptimizer()
+        assert optimizer.supports_f_abs_tol() is True
+
+        optimizer.set_f_abs_tol(1e-5)
+        assert optimizer.options["ftol_abs"] == 1e-5
+
+    def test_fides_optimizer_support(self):
+        """Test FidesOptimizer tolerance support."""
+        optimizer = optimize.FidesOptimizer()
+        assert optimizer.supports_f_abs_tol() is True
+
+        optimizer.set_f_abs_tol(1e-6)
+
+        from fides.constants import Options as FidesOptions
+
+        assert FidesOptions.FATOL in optimizer.options
+        assert optimizer.options[FidesOptions.FATOL] == 1e-6
+
+        # Test updating existing value
+        optimizer.set_f_abs_tol(1e-9)
+        assert optimizer.options[FidesOptions.FATOL] == 1e-9
+
+    def test_cma_optimizer_support(self):
+        """Test CmaOptimizer tolerance support."""
+        optimizer = optimize.CmaOptimizer()
+        assert optimizer.supports_f_abs_tol() is True
+
+        optimizer.set_f_abs_tol(1e-4)
+        assert optimizer.options["tolfun"] == 1e-4
+
+    def test_scipy_de_optimizer_support(self):
+        """Test ScipyDifferentialEvolutionOptimizer tolerance support."""
+        optimizer = optimize.ScipyDifferentialEvolutionOptimizer()
+        assert optimizer.supports_f_abs_tol() is True
+
+        optimizer.set_f_abs_tol(1e-5)
+        assert optimizer.options["atol"] == 1e-5
+
+    def test_pyswarm_optimizer_support(self):
+        """Test PyswarmOptimizer tolerance support."""
+        optimizer = optimize.PyswarmOptimizer()
+        assert optimizer.supports_f_abs_tol() is True
+
+        optimizer.set_f_abs_tol(1e-7)
+        assert optimizer.options["minfunc"] == 1e-7
+
+    def test_dlib_optimizer_no_support(self):
+        """Test that DlibOptimizer does not support tolerance."""
+        optimizer = optimize.DlibOptimizer()
+        assert optimizer.supports_f_abs_tol() is False
+
+        with pytest.raises(NotImplementedError):
+            optimizer.set_f_abs_tol(1e-6)
+
+    def test_pyswarms_optimizer_no_support(self):
+        """Test that PyswarmsOptimizer does not support tolerance."""
+        optimizer = optimize.PyswarmsOptimizer()
+        assert optimizer.supports_f_abs_tol() is False
+
+        with pytest.raises(NotImplementedError):
+            optimizer.set_f_abs_tol(1e-6)
+
+    def test_tolerance_validation(self):
+        """Test that invalid tolerance values are rejected."""
+        optimizer = optimize.ScipyOptimizer()
+
+        # Test that positive values work
+        optimizer.set_f_abs_tol(1e-6)
+        assert optimizer.tol == 1e-6
+
+        # Test that zero is allowed (optimize as accurately as possible)
+        optimizer.set_f_abs_tol(0.0)
+        assert optimizer.tol == 0.0
+
+        # Test that negative values are rejected
+        with pytest.raises(ValueError, match="must be non-negative"):
+            optimizer.set_f_abs_tol(-1e-6)