diff --git a/examples/max_flow.rs b/examples/max_flow.rs
index 215d38a1..294434d2 100644
--- a/examples/max_flow.rs
+++ b/examples/max_flow.rs
@@ -143,7 +143,7 @@ where
     F: SparseElement<F> + Zero + Eq + NonZero,
 {
     type Column = Column;
-    type Cost<'a> = Cost;
+    type Cost<'a> where Self: 'a = Cost;
     type Rhs = F;
 
     fn column(&self, j: usize) -> Self::Column {
diff --git a/src/algorithm/mod.rs b/src/algorithm/mod.rs
index edb8c5c7..5ba4a882 100644
--- a/src/algorithm/mod.rs
+++ b/src/algorithm/mod.rs
@@ -22,16 +22,16 @@ pub trait SolveRelaxation: MatrixProvider {
     /// # Return value
     /// 
     /// Whether the problem is feasible, and if so, a solution if the problem is bounded.
-    fn solve_relaxation<IM>(&self) -> OptimizationResult<IM::F>
+    fn solve_relaxation<'provider, IM>(&'provider self) -> OptimizationResult<IM::F>
     where
         IM: InverseMaintener<F:
             im_ops::FieldHR +
             im_ops::Column<<Self::Column as Column>::F> +
             im_ops::Cost<ArtificialCost> +
+            im_ops::Cost<Self::Cost<'provider>> +
             im_ops::Rhs<Self::Rhs> +
             im_ops::Column<Self::Rhs> +
         >,
-        for<'r> IM::F: im_ops::Cost<Self::Cost<'r>>,
     ;
 }
 
diff --git a/src/algorithm/two_phase/matrix_provider/column/mod.rs b/src/algorithm/two_phase/matrix_provider/column/mod.rs
index 6c1a3360..3360cf20 100644
--- a/src/algorithm/two_phase/matrix_provider/column/mod.rs
+++ b/src/algorithm/two_phase/matrix_provider/column/mod.rs
@@ -36,7 +36,7 @@ pub trait Column: ColumnIntoIterator<Self::F> + Debug {
     /// Type of struct to iterate over this column.
     ///
     /// It should be somewhat cheaply cloneable and as such not be too large.
-    type Iter<'a>: ColumnIterator<'a, F=Self::F>;
+    type Iter<'a>: ColumnIterator<'a, F=Self::F> where Self: 'a;
 
     /// Derive the iterator object.
     ///
diff --git a/src/algorithm/two_phase/matrix_provider/filter/generic_wrapper.rs b/src/algorithm/two_phase/matrix_provider/filter/generic_wrapper.rs
index a7e2b529..069edb4b 100644
--- a/src/algorithm/two_phase/matrix_provider/filter/generic_wrapper.rs
+++ b/src/algorithm/two_phase/matrix_provider/filter/generic_wrapper.rs
@@ -226,7 +226,7 @@ where
     MP: MatrixProvider<Column: IntoFilteredColumn>,
 {
     type Column = <MP::Column as IntoFilteredColumn>::Filtered;
-    type Cost<'a> = MP::Cost<'a>;
+    type Cost<'a> where Self: 'a = MP::Cost<'provider>;
     type Rhs = MP::Rhs;
 
     fn column(&self, j: usize) -> Self::Column {
diff --git a/src/algorithm/two_phase/matrix_provider/filter/mod.rs b/src/algorithm/two_phase/matrix_provider/filter/mod.rs
index 1d55f361..f26c573a 100644
--- a/src/algorithm/two_phase/matrix_provider/filter/mod.rs
+++ b/src/algorithm/two_phase/matrix_provider/filter/mod.rs
@@ -18,7 +18,7 @@ pub trait Filtered: MatrixProvider {
 /// Derive a variant of the matrix provider that has rows removed from it.
 pub trait ToFiltered: MatrixProvider {
     /// The resulting matrix provider type.
-    type Filtered<'provider>: Filtered<Column: Column<F=<Self::Column as Column>::F>>;
+    type Filtered<'provider>: Filtered<Column: Column<F=<Self::Column as Column>::F>> where Self: 'provider;
 
     /// Derive a variant of the matrix provider that has rows removed from it.
     ///
diff --git a/src/algorithm/two_phase/matrix_provider/matrix_data.rs b/src/algorithm/two_phase/matrix_provider/matrix_data.rs
index 05661eb2..fd630199 100644
--- a/src/algorithm/two_phase/matrix_provider/matrix_data.rs
+++ b/src/algorithm/two_phase/matrix_provider/matrix_data.rs
@@ -284,7 +284,7 @@ where
     for<'r> &'r F: FieldRef<F>,
 {
     type Column = Column<F>;
-    type Cost<'a> = Option<&'a <Self::Column as ColumnTrait>::F>;
+    type Cost<'a> where Self: 'a = Option<&'a <Self::Column as ColumnTrait>::F>;
     type Rhs = F;
 
     #[inline]
diff --git a/src/algorithm/two_phase/matrix_provider/mod.rs b/src/algorithm/two_phase/matrix_provider/mod.rs
index f8b3b5d8..8274af37 100644
--- a/src/algorithm/two_phase/matrix_provider/mod.rs
+++ b/src/algorithm/two_phase/matrix_provider/mod.rs
@@ -45,7 +45,7 @@ pub trait MatrixProvider {
     ///
     /// This type will often be of the form `Option<_>` so to not have to store any zero values, the
     /// inner type would never be zero in that case.
-    type Cost<'a>;
+    type Cost<'a> where Self: 'a;
 
     /// Right hand side type.
     type Rhs: ops::Rhs;
diff --git a/src/algorithm/two_phase/mod.rs b/src/algorithm/two_phase/mod.rs
index cebba80f..5ee5530d 100644
--- a/src/algorithm/two_phase/mod.rs
+++ b/src/algorithm/two_phase/mod.rs
@@ -27,15 +27,15 @@ where
     MP: MatrixProvider<Column: Identity + IntoFilteredColumn>,
 {
     // TODO(ENHANCEMENT): Specialize for MatrixProviders that can be filtered directly.
-    default fn solve_relaxation<IM>(&self) -> OptimizationResult<IM::F>
+    default fn solve_relaxation<'provider, IM>(&'provider self) -> OptimizationResult<IM::F>
     where
         IM: InverseMaintener<F:
             im_ops::FieldHR +
             im_ops::Column<<<Self as MatrixProvider>::Column as Column>::F> +
             im_ops::Cost<ArtificialCost> +
+            im_ops::Cost<MP::Cost<'provider>> +
             im_ops::Rhs<MP::Rhs> +
         >,
-        for<'r> IM::F: im_ops::Cost<MP::Cost<'r>>,
     {
         match self.compute_bfs_giving_im::<IM>() {
             RankedFeasibilityResult::Feasible {
@@ -84,15 +84,15 @@ where
     MP: MatrixProvider<Column: Identity + IntoFilteredColumn>,
     MP::Rhs: 'static + ColumnNumber,
 {
-    fn solve_relaxation<IM>(&self) -> OptimizationResult<IM::F>
+    fn solve_relaxation<'provider, IM>(&'provider self) -> OptimizationResult<IM::F>
     where
         IM: InverseMaintener<F:
             im_ops::FieldHR +
             im_ops::Column<<<Self as MatrixProvider>::Column as Column>::F> +
+            im_ops::Cost<MP::Cost<'provider>> +
             im_ops::Rhs<Self::Rhs> +
             im_ops::Column<Self::Rhs> +
         >,
-        for<'r> IM::F: im_ops::Cost<MP::Cost<'r>>,
     {
         let basis_indices = self.pivot_element_indices();
         // Sorting of identity matrix columns
diff --git a/src/algorithm/two_phase/phase_two.rs b/src/algorithm/two_phase/phase_two.rs
index c96b1824..7436c4a0 100644
--- a/src/algorithm/two_phase/phase_two.rs
+++ b/src/algorithm/two_phase/phase_two.rs
@@ -19,12 +19,15 @@ use crate::algorithm::two_phase::tableau::kind::non_artificial::NonArtificial;
 ///
 /// An `OptimizationResult` indicating whether or not the problem has a finite optimum. It cannot be
 /// infeasible, as a feasible solution is needed to start using this method.
-pub fn primal<IM, MP, PR>(
-    tableau: &mut Tableau<IM, NonArtificial<MP>>,
+pub fn primal<'provider, IM, MP, PR>(
+    tableau: &mut Tableau<IM, NonArtificial<'provider, MP>>,
 ) -> OptimizationResult<IM::F>
 where
-    IM: InverseMaintener<F: im_ops::FieldHR + im_ops::Column<<MP::Column as Column>::F>>,
-    for<'r> IM::F: im_ops::Cost<MP::Cost<'r>>,
+    IM: InverseMaintener<F:
+        im_ops::FieldHR +
+        im_ops::Column<<MP::Column as Column>::F> +
+        im_ops::Cost<MP::Cost<'provider>> +
+    >,
     MP: MatrixProvider,
     PR: PivotRule<IM::F>,
 {
diff --git a/src/data/linear_algebra/vector/sparse.rs b/src/data/linear_algebra/vector/sparse.rs
index 924873ac..867c751c 100644
--- a/src/data/linear_algebra/vector/sparse.rs
+++ b/src/data/linear_algebra/vector/sparse.rs
@@ -203,7 +203,7 @@ where
     C: SparseComparator,
 {
     type F = F;
-    type Iter<'a> = SparseSliceIterator<'a, F>;
+    type Iter<'a> where C: 'a = SparseSliceIterator<'a, F>;
 
     fn iter(&self) -> Self::Iter<'_> {
         SparseSliceIterator::new(&self.data)
diff --git a/src/tests/problem_1.rs b/src/tests/problem_1.rs
index a9bb9b30..0f2571fe 100644
--- a/src/tests/problem_1.rs
+++ b/src/tests/problem_1.rs
@@ -402,11 +402,11 @@ pub fn artificial_tableau_form<MP: MatrixProvider<Column: ColumnTrait<F=T>, Rhs=
     )
 }
 
-pub fn tableau_form<MP: MatrixProvider<Column: ColumnTrait<F=T>>>(
-    provider: &MP,
+pub fn tableau_form<'provider, MP: MatrixProvider<Column: ColumnTrait<F=T>>>(
+    provider: &'provider MP,
 ) -> Tableau<Carry<S, BasisInverseRows<S>>, NonArtificial<MP>>
 where
-    for<'a> S: im_ops::Cost<MP::Cost<'a>>,
+    S: im_ops::Cost<MP::Cost<'provider>>,
 {
     let carry = {
         let minus_objective = RB!(-58);