diff --git a/include/ensmallen_bits/fw/atoms.hpp b/include/ensmallen_bits/fw/atoms.hpp
index b77cc6f52..8a72c6c32 100644
--- a/include/ensmallen_bits/fw/atoms.hpp
+++ b/include/ensmallen_bits/fw/atoms.hpp
@@ -114,7 +114,7 @@ class Atoms
       // add an atom norm constraint, you could use projected gradient method,
       // see the implementaton of ProjectedGradientEnhancement().
       arma::vec newCoeffs =
-          solve(function.MatrixA() * newAtoms, function.Vectorb());
+          solve(function.MatrixA() * newAtoms, function.Vectorb(), arma::solve_opts::fast);
 
       // Evaluate the function again.
       double Fnew = function.Evaluate(newAtoms * newCoeffs);
diff --git a/include/ensmallen_bits/fw/update_span.hpp b/include/ensmallen_bits/fw/update_span.hpp
index 5862d3dc3..1c113d881 100644
--- a/include/ensmallen_bits/fw/update_span.hpp
+++ b/include/ensmallen_bits/fw/update_span.hpp
@@ -57,7 +57,7 @@ class UpdateSpan
 
     // Reoptimize the solution in the current space.
     arma::vec b = function.Vectorb();
-    atoms.CurrentCoeffs() = solve(function.MatrixA() * atoms.CurrentAtoms(), b);
+    atoms.CurrentCoeffs() = solve(function.MatrixA() * atoms.CurrentAtoms(), b, arma::solve_opts::fast);
 
     // x has coords of only the current atoms, recover the solution
     // to the original size.
diff --git a/include/ensmallen_bits/sdp/primal_dual_impl.hpp b/include/ensmallen_bits/sdp/primal_dual_impl.hpp
index bddd6642c..88e7b1e37 100644
--- a/include/ensmallen_bits/sdp/primal_dual_impl.hpp
+++ b/include/ensmallen_bits/sdp/primal_dual_impl.hpp
@@ -197,8 +197,7 @@ SolveKKTSystem(const SparseConstraintType& aSparse,
   if (aDense.n_rows)
     rhs(arma::span(aSparse.n_rows, numConstraints - 1), 0) += aDense * eInvFrdRc;
 
-  // TODO(stephentu): use a more efficient method (e.g. LU decomposition)
-  if (!arma::solve(dy, m, rhs))
+  if (!arma::solve(dy, m, rhs, arma::solve_opts::fast))
   {
     throw std::logic_error("PrimalDualSolver::SolveKKTSystem(): Could not "
         "solve KKT system.");