diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt
index 862b7cf..e094f6a 100644
--- a/internal/ceres/CMakeLists.txt
+++ b/internal/ceres/CMakeLists.txt
@@ -55,6 +55,7 @@
     file.cc
     gradient_checking_cost_function.cc
     implicit_schur_complement.cc
+    inner_iteration_minimizer.cc
     iterative_schur_complement_solver.cc
     levenberg_marquardt_strategy.cc
     linear_least_squares_problems.cc
diff --git a/internal/ceres/inner_iteration_minimizer.cc b/internal/ceres/inner_iteration_minimizer.cc
new file mode 100644
index 0000000..6a9b419
--- /dev/null
+++ b/internal/ceres/inner_iteration_minimizer.cc
@@ -0,0 +1,256 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include "ceres/inner_iteration_minimizer.h"
+
+#include <numeric>
+#include <vector>
+#include "ceres/evaluator.h"
+#include "ceres/linear_solver.h"
+#include "ceres/minimizer.h"
+#include "ceres/ordering.h"
+#include "ceres/parameter_block.h"
+#include "ceres/problem_impl.h"
+#include "ceres/program.h"
+#include "ceres/residual_block.h"
+#include "ceres/schur_ordering.h"
+#include "ceres/solver.h"
+#include "ceres/solver_impl.h"
+#include "ceres/trust_region_minimizer.h"
+#include "ceres/trust_region_strategy.h"
+
+namespace ceres {
+namespace internal {
+
+InnerIterationMinimizer::~InnerIterationMinimizer() {
+}
+
+bool InnerIterationMinimizer::Init(const Program& outer_program,
+                                   const ProblemImpl::ParameterMap& parameter_map,
+                                   const vector<double*>& parameter_blocks_for_inner_iterations,
+                                   string* error) {
+  program_.reset(new Program(outer_program));
+
+  Ordering ordering;
+  int num_inner_iteration_parameter_blocks = 0;
+
+  if (parameter_blocks_for_inner_iterations.size() == 0) {
+    // The user wishes for the solver to determine a set of parameter
+    // blocks to descend on.
+    //
+    // For now use approximate maximum independent set computed by
+    // ComputeSchurOrdering code. Though going forward, we want use
+    // the smallest maximal independent set, rather than the largest.
+    //
+    // TODO(sameeragarwal): Smallest maximal independent set instead
+    // of the approximate maximum independent set.
+    vector<ParameterBlock*> parameter_block_ordering;
+    num_inner_iteration_parameter_blocks =
+        ComputeSchurOrdering(*program_, &parameter_block_ordering);
+    // Decompose the Schur ordering into elimination group 0 and 1, 0
+    // is the one used for inner iterations.
+    for (int i = 0; i < parameter_block_ordering.size(); ++i) {
+      double* ptr = parameter_block_ordering[i]->mutable_user_state();
+      if (i < num_inner_iteration_parameter_blocks) {
+        ordering.AddParameterBlockToGroup(ptr, 0);
+      } else {
+        ordering.AddParameterBlockToGroup(ptr, 1);
+      }
+    }
+  } else {
+    const vector<ParameterBlock*> parameter_blocks = program_->parameter_blocks();
+    set<double*> parameter_block_ptrs(parameter_blocks_for_inner_iterations.begin(),
+                                      parameter_blocks_for_inner_iterations.end());
+    num_inner_iteration_parameter_blocks = 0;
+    // Divide the set of parameter blocks into two groups. Group 0 is
+    // the set of parameter blocks specified by the user, and the rest
+    // in group 1.
+    for (int i = 0; i < parameter_blocks.size(); ++i) {
+      double* ptr = parameter_blocks[i]->mutable_user_state();
+      if (parameter_block_ptrs.count(ptr) != 0) {
+        ordering.AddParameterBlockToGroup(ptr, 0);
+      } else {
+        ordering.AddParameterBlockToGroup(ptr, 1);
+      }
+    }
+
+    num_inner_iteration_parameter_blocks = ordering.GroupSize(0);
+    if (num_inner_iteration_parameter_blocks > 0) {
+      const map<int, set<double*> >& group_id_to_parameter_blocks =
+          ordering.group_id_to_parameter_blocks();
+      if (!SolverImpl::IsParameterBlockSetIndependent(
+              group_id_to_parameter_blocks.begin()->second,
+              program_->residual_blocks())) {
+        *error = "The user provided parameter_blocks_for_inner_iterations "
+            "does not form an independent set";
+        return false;
+      }
+    }
+  }
+
+  if (!SolverImpl::ApplyUserOrdering(parameter_map,
+                                     &ordering,
+                                     program_.get(),
+                                     error)) {
+    return false;
+  }
+
+  program_->SetParameterOffsetsAndIndex();
+
+  if (!SolverImpl::LexicographicallyOrderResidualBlocks(
+          num_inner_iteration_parameter_blocks,
+          program_.get(),
+          error)) {
+    return false;
+  }
+
+  ComputeResidualBlockOffsets(num_inner_iteration_parameter_blocks);
+
+  const_cast<Program*>(&outer_program)->SetParameterOffsetsAndIndex();
+
+  LinearSolver::Options linear_solver_options;
+  linear_solver_options.type = DENSE_QR;
+  linear_solver_.reset(LinearSolver::Create(linear_solver_options));
+  CHECK_NOTNULL(linear_solver_.get());
+
+  evaluator_options_.linear_solver_type = DENSE_QR;
+  evaluator_options_.num_eliminate_blocks = 0;
+  evaluator_options_.num_threads = 1;
+
+  return true;
+}
+
+void InnerIterationMinimizer::Minimize(
+    const Minimizer::Options& options,
+    double* parameters,
+    Solver::Summary* summary) {
+  const vector<ParameterBlock*>& parameter_blocks = program_->parameter_blocks();
+  const vector<ResidualBlock*>& residual_blocks = program_->residual_blocks();
+
+  const int num_inner_iteration_parameter_blocks = residual_block_offsets_.size() - 1;
+
+  for (int i = 0; i < parameter_blocks.size(); ++i) {
+    ParameterBlock* parameter_block = parameter_blocks[i];
+    parameter_block->SetState(parameters + parameter_block->state_offset());
+    if (i >=  num_inner_iteration_parameter_blocks) {
+      parameter_block->SetConstant();
+    }
+  }
+
+#pragma omp parallel for num_threads(options.num_threads)
+  for (int i = 0; i < num_inner_iteration_parameter_blocks; ++i) {
+    Solver::Summary inner_summary;
+    ParameterBlock* parameter_block = parameter_blocks[i];
+    const int old_index = parameter_block->index();
+    const int old_delta_offset = parameter_block->delta_offset();
+
+    parameter_block->set_index(0);
+    parameter_block->set_delta_offset(0);
+
+    Program inner_program;
+    inner_program.mutable_parameter_blocks()->push_back(parameter_block);
+
+    // This works, because we have already ordered the residual blocks
+    // so that the residual blocks for each parameter block being
+    // optimized over are contiguously located in the residual_blocks
+    // vector.
+    copy(residual_blocks.begin() + residual_block_offsets_[i],
+         residual_blocks.begin() + residual_block_offsets_[i + 1],
+         back_inserter(*inner_program.mutable_residual_blocks()));
+
+    MinimalSolve(&inner_program,
+                 parameters + parameter_block->state_offset(),
+                 &inner_summary);
+
+    parameter_block->set_index(old_index);
+    parameter_block->set_delta_offset(old_delta_offset);
+  }
+
+  for (int i =  num_inner_iteration_parameter_blocks; i < parameter_blocks.size(); ++i) {
+    parameter_blocks[i]->SetVarying();
+  }
+}
+
+void InnerIterationMinimizer::MinimalSolve(Program* program,
+                                           double* parameters,
+                                           Solver::Summary* summary) {
+
+  *summary = Solver::Summary();
+  summary->initial_cost = 0.0;
+  summary->fixed_cost = 0.0;
+  summary->final_cost = 0.0;
+  string error;
+
+  scoped_ptr<Evaluator> evaluator(Evaluator::Create(evaluator_options_, program,  &error));
+  CHECK_NOTNULL(evaluator.get());
+
+  scoped_ptr<SparseMatrix> jacobian(evaluator->CreateJacobian());
+  CHECK_NOTNULL(jacobian.get());
+
+  TrustRegionStrategy::Options trust_region_strategy_options;
+  trust_region_strategy_options.linear_solver = linear_solver_.get();
+  scoped_ptr<TrustRegionStrategy>trust_region_strategy(
+      TrustRegionStrategy::Create(trust_region_strategy_options));
+  CHECK_NOTNULL(trust_region_strategy.get());
+
+  Minimizer::Options minimizer_options;
+  minimizer_options.evaluator = evaluator.get();
+  minimizer_options.jacobian = jacobian.get();
+  minimizer_options.trust_region_strategy = trust_region_strategy.get();
+
+  TrustRegionMinimizer minimizer;
+  minimizer.Minimize(minimizer_options, parameters, summary);
+}
+
+
+void InnerIterationMinimizer::ComputeResidualBlockOffsets(
+    const int num_eliminate_blocks) {
+  vector<int> counts(num_eliminate_blocks, 0);
+  const vector<ResidualBlock*>& residual_blocks = program_->residual_blocks();
+  for (int i = 0; i < residual_blocks.size(); ++i) {
+    ResidualBlock* residual_block = residual_blocks[i];
+    const int num_parameter_blocks = residual_block->NumParameterBlocks();
+    for (int j = 0; j < num_parameter_blocks; ++j) {
+      ParameterBlock* parameter_block = residual_block->parameter_blocks()[j];
+      if (!parameter_block->IsConstant() &&
+          parameter_block->index() < num_eliminate_blocks) {
+        counts[parameter_block->index()] += 1;
+      }
+    }
+  }
+
+  residual_block_offsets_.resize(num_eliminate_blocks + 1);
+  residual_block_offsets_[0] = 0;
+  partial_sum(counts.begin(), counts.end(), residual_block_offsets_.begin() + 1);
+}
+
+
+}  // namespace internal
+}  // namespace ceres
diff --git a/internal/ceres/inner_iteration_minimizer.h b/internal/ceres/inner_iteration_minimizer.h
new file mode 100644
index 0000000..b7c7461
--- /dev/null
+++ b/internal/ceres/inner_iteration_minimizer.h
@@ -0,0 +1,87 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include <vector>
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/minimizer.h"
+#include "ceres/problem_impl.h"
+#include "ceres/solver.h"
+#include "ceres/trust_region_strategy.h"
+#include "ceres/evaluator.h"
+#include "ceres/linear_solver.h"
+
+namespace ceres {
+namespace internal {
+
+class Program;
+
+// The InnerIterationMinimizer performs coordinate descent on a user
+// specified set of parameter blocks. The user can either specify the
+// set of parameter blocks for coordinate descent or have the
+// minimizer choose on its own.
+//
+// This Minimizer when used in combination with the
+// TrustRegionMinimizer is used to implement a non-linear
+// generalization of Ruhe & Wedin's Algorithm II for separable
+// non-linear least squares problems.
+class InnerIterationMinimizer : public Minimizer {
+ public:
+  // Initialize the minimizer. The return value indicates success or
+  // failure, and the error string contains a description of the
+  // error.
+  //
+  // The parameter blocks for inner iterations must form an
+  // independent set in the Hessian for the optimization problem.
+  //
+  // If this vector is empty, the minimizer will attempt to find a set
+  // of parameter blocks to optimize.
+  bool Init(const Program& program,
+            const ProblemImpl::ParameterMap& parameter_map,
+            const vector<double*>& parameter_blocks_for_inner_iterations,
+            string* error);
+
+  // Minimizer interface.
+  virtual ~InnerIterationMinimizer();
+  virtual void Minimize(const Minimizer::Options& options,
+                        double* parameters,
+                        Solver::Summary* summary);
+
+ private:
+  void MinimalSolve(Program* program, double* parameters, Solver::Summary* summary);
+  void ComputeResidualBlockOffsets(const int num_eliminate_blocks);
+
+  scoped_ptr<Program> program_;
+  vector<int> residual_block_offsets_;
+  Evaluator::Options evaluator_options_;
+  scoped_ptr<LinearSolver> linear_solver_;
+};
+
+}  // namespace internal
+}  // namespace ceres
diff --git a/internal/ceres/minimizer.h b/internal/ceres/minimizer.h
index 667d80a..22c10f0 100644
--- a/internal/ceres/minimizer.h
+++ b/internal/ceres/minimizer.h
@@ -59,6 +59,7 @@
     }
 
     void Init(const Solver::Options& options) {
+      num_threads = options.num_threads;
       max_num_iterations = options.max_num_iterations;
       max_solver_time_in_seconds = options.max_solver_time_in_seconds;
       max_step_solver_retries = 5;
@@ -81,6 +82,7 @@
       trust_region_strategy = NULL;
       jacobian = NULL;
       callbacks = options.callbacks;
+      inner_iteration_minimizer = NULL;
     }
 
     int max_num_iterations;
@@ -91,6 +93,7 @@
     // mu at each retry. This leads to stronger and stronger
     // regularization making the linear least squares problem better
     // conditioned at each retry.
+    int num_threads;
     int max_step_solver_retries;
     double gradient_tolerance;
     double parameter_tolerance;
@@ -126,6 +129,8 @@
     // and will remain constant for the life time of the
     // optimization. The Options struct does not own this pointer.
     SparseMatrix* jacobian;
+
+    Minimizer* inner_iteration_minimizer;
   };
 
   virtual ~Minimizer() {}
diff --git a/internal/ceres/parameter_block.h b/internal/ceres/parameter_block.h
index dd69cd6..f20805c 100644
--- a/internal/ceres/parameter_block.h
+++ b/internal/ceres/parameter_block.h
@@ -112,6 +112,10 @@
   int index() const { return index_; }
   void set_index(int index) { index_ = index; }
 
+  // This parameter offset inside a larger state vector.
+  int state_offset() const { return state_offset_; }
+  void set_state_offset(int state_offset) { state_offset_ = state_offset; }
+
   // This parameter offset inside a larger delta vector.
   int delta_offset() const { return delta_offset_; }
   void set_delta_offset(int delta_offset) { delta_offset_ = delta_offset; }
@@ -172,13 +176,14 @@
 
   string ToString() const {
     return StringPrintf("{ user_state=%p, state=%p, size=%d, "
-                        "constant=%d, index=%d, "
+                        "constant=%d, index=%d, state_offset=%d, "
                         "delta_offset=%d }",
                         user_state_,
                         state_,
                         size_,
                         is_constant_,
                         index_,
+                        state_offset_,
                         delta_offset_);
   }
 
@@ -197,6 +202,7 @@
     }
 
     index_ = -1;
+    state_offset_ = -1;
     delta_offset_ = -1;
   }
 
@@ -249,6 +255,9 @@
   // permit switching from a ParameterBlock* to an index in another array.
   int32 index_;
 
+  // The offset of this parameter block inside a larger state vector.
+  int32 state_offset_;
+
   // The offset of this parameter block inside a larger delta vector.
   int32 delta_offset_;
 
diff --git a/internal/ceres/problem_test.cc b/internal/ceres/problem_test.cc
index 9b20dca..4afe1b5 100644
--- a/internal/ceres/problem_test.cc
+++ b/internal/ceres/problem_test.cc
@@ -275,6 +275,7 @@
   EXPECT_EQ(12, problem.NumParameters());
 
   // Add a parameter that has a local parameterization.
+  w[0] = 1.0; w[1] = 0.0; w[2] = 0.0; w[3] = 0.0;
   problem.AddParameterBlock(w, 4, new QuaternionParameterization);
   EXPECT_EQ(4,  problem.NumParameterBlocks());
   EXPECT_EQ(16, problem.NumParameters());
diff --git a/internal/ceres/program.cc b/internal/ceres/program.cc
index 99f6af9..82d76d3 100644
--- a/internal/ceres/program.cc
+++ b/internal/ceres/program.cc
@@ -129,10 +129,13 @@
     }
   }
   // For parameters that appear in the program, set their position and offset.
+  int state_offset = 0;
   int delta_offset = 0;
   for (int i = 0; i < parameter_blocks_.size(); ++i) {
     parameter_blocks_[i]->set_index(i);
+    parameter_blocks_[i]->set_state_offset(state_offset);
     parameter_blocks_[i]->set_delta_offset(delta_offset);
+    state_offset += parameter_blocks_[i]->Size();
     delta_offset += parameter_blocks_[i]->LocalSize();
   }
 }
diff --git a/internal/ceres/program_evaluator.h b/internal/ceres/program_evaluator.h
index 6c48e7d..1fb44e1 100644
--- a/internal/ceres/program_evaluator.h
+++ b/internal/ceres/program_evaluator.h
@@ -129,7 +129,7 @@
 
     if (residuals != NULL) {
       VectorRef(residuals, program_->NumResiduals()).setZero();
-    } 
+    }
 
     if (jacobian != NULL) {
       jacobian->SetZero();
diff --git a/internal/ceres/solver_impl.cc b/internal/ceres/solver_impl.cc
index c45c194..4f914fa 100644
--- a/internal/ceres/solver_impl.cc
+++ b/internal/ceres/solver_impl.cc
@@ -36,6 +36,7 @@
 #include "ceres/evaluator.h"
 #include "ceres/gradient_checking_cost_function.h"
 #include "ceres/iteration_callback.h"
+#include "ceres/inner_iteration_minimizer.h"
 #include "ceres/levenberg_marquardt_strategy.h"
 #include "ceres/linear_solver.h"
 #include "ceres/map_util.h"
@@ -150,6 +151,7 @@
 
 void SolverImpl::Minimize(const Solver::Options& options,
                           Program* program,
+                          InnerIterationMinimizer* inner_iteration_minimizer,
                           Evaluator* evaluator,
                           LinearSolver* linear_solver,
                           double* parameters,
@@ -182,6 +184,7 @@
   minimizer_options.evaluator = evaluator;
   scoped_ptr<SparseMatrix> jacobian(evaluator->CreateJacobian());
   minimizer_options.jacobian = jacobian.get();
+  minimizer_options.inner_iteration_minimizer = inner_iteration_minimizer;
 
   TrustRegionStrategy::Options trust_region_strategy_options;
   trust_region_strategy_options.linear_solver = linear_solver;
@@ -214,6 +217,11 @@
   // Reset the summary object to its default values.
   *CHECK_NOTNULL(summary) = Solver::Summary();
 
+  if (options.lsqp_iterations_to_dump.size() > 0) {
+    LOG(WARNING) << "Dumping linear least squares problems to disk is"
+        " currently broken. Ignoring Solver::Options::lsqp_iterations_to_dump";
+  }
+
 #ifndef CERES_USE_OPENMP
   if (options.num_threads > 1) {
     LOG(WARNING)
@@ -323,16 +331,35 @@
     return;
   }
 
-  if (!MaybeReorderResidualBlocks(options,
-                                  reduced_program.get(),
-                                  &summary->error)) {
+  // Only Schur types require the lexicographic reordering.
+  if (IsSchurType(options.linear_solver_type)) {
+    const int num_eliminate_blocks =
+        options.ordering->group_id_to_parameter_blocks().begin()->second.size();
+    if (!LexicographicallyOrderResidualBlocks(num_eliminate_blocks,
+                                              reduced_program.get(),
+                                              &summary->error)) {
+      return;
+    }
+  }
+
+  scoped_ptr<Evaluator> evaluator(CreateEvaluator(options,
+                                                  problem_impl->parameter_map(),
+                                                  reduced_program.get(),
+                                                  &summary->error));
+  if (evaluator == NULL) {
     return;
   }
 
-  scoped_ptr<Evaluator> evaluator(
-      CreateEvaluator(options, reduced_program.get(), &summary->error));
-  if (evaluator == NULL) {
-    return;
+  scoped_ptr<InnerIterationMinimizer> inner_iteration_minimizer;
+  if (options.use_inner_iterations) {
+    inner_iteration_minimizer.reset(new InnerIterationMinimizer);
+    if (!inner_iteration_minimizer->Init(
+            *reduced_program,
+            problem_impl->parameter_map(),
+            options.parameter_blocks_for_inner_iterations,
+            &summary->error)) {
+      return;
+    }
   }
 
   // The optimizer works on contiguous parameter vectors; allocate some.
@@ -348,6 +375,7 @@
   // Run the optimization.
   Minimize(options,
            reduced_program.get(),
+           inner_iteration_minimizer.get(),
            evaluator.get(),
            linear_solver.get(),
            parameters.data(),
@@ -412,33 +440,41 @@
       options.ordering->NumGroups() > 1) {
     const set<double*>& e_blocks  =
         options.ordering->group_id_to_parameter_blocks().begin()->second;
-
-    // Loop over each residual block and ensure that no two parameter
-    // blocks in the same residual block are part of the first
-    // elimination group, as that would violate the assumption that it
-    // is an independent set in the Hessian matrix.
-    for (vector<ResidualBlock*>::const_iterator it = residual_blocks.begin();
-         it != residual_blocks.end();
-         ++it) {
-      ParameterBlock* const* parameter_blocks = (*it)->parameter_blocks();
-      const int num_parameter_blocks = (*it)->NumParameterBlocks();
-      int count = 0;
-      for (int i = 0; i < num_parameter_blocks; ++i) {
-        count += e_blocks.count(const_cast<double*>(
-                                    parameter_blocks[i]->user_state()));
-      }
-
-      if (count > 1) {
-        *error = "The user requested the use of a Schur type solver. "
-            "But the first elimination group in the ordering is not an "
-            "independent set.";
-        return false;
-      }
+    if (!IsParameterBlockSetIndependent(e_blocks, residual_blocks)) {
+      *error = "The user requested the use of a Schur type solver. "
+          "But the first elimination group in the ordering is not an "
+          "independent set.";
+      return false;
     }
   }
   return true;
 }
 
+bool SolverImpl::IsParameterBlockSetIndependent(const set<double*> parameter_block_ptrs,
+                                                const vector<ResidualBlock*> residual_blocks) {
+  // Loop over each residual block and ensure that no two parameter
+  // blocks in the same residual block are part of
+  // parameter_block_ptrs as that would violate the assumption that it
+  // is an independent set in the Hessian matrix.
+  for (vector<ResidualBlock*>::const_iterator it = residual_blocks.begin();
+       it != residual_blocks.end();
+       ++it) {
+    ParameterBlock* const* parameter_blocks = (*it)->parameter_blocks();
+    const int num_parameter_blocks = (*it)->NumParameterBlocks();
+    int count = 0;
+    for (int i = 0; i < num_parameter_blocks; ++i) {
+      count +=
+          parameter_block_ptrs.count(const_cast<double*>(
+                                         parameter_blocks[i]->user_state()));
+    }
+    if (count > 1) {
+      return false;
+    }
+  }
+  return true;
+}
+
+
 // Strips varying parameters and residuals, maintaining order, and updating
 // num_eliminate_blocks.
 bool SolverImpl::RemoveFixedBlocksFromProgram(Program* program,
@@ -572,8 +608,10 @@
     }
   }
 
-  if (!ApplyUserOrdering(
-          *problem_impl, ordering, transformed_program.get(), error)) {
+  if (!ApplyUserOrdering(problem_impl->parameter_map(),
+                         ordering,
+                         transformed_program.get(),
+                         error)) {
     return NULL;
   }
 
@@ -744,7 +782,7 @@
   return LinearSolver::Create(linear_solver_options);
 }
 
-bool SolverImpl::ApplyUserOrdering(const ProblemImpl& problem_impl,
+bool SolverImpl::ApplyUserOrdering(const ProblemImpl::ParameterMap& parameter_map,
                                    const Ordering* ordering,
                                    Program* program,
                                    string* error) {
@@ -761,8 +799,6 @@
       program->mutable_parameter_blocks();
   parameter_blocks->clear();
 
-  const ProblemImpl::ParameterMap& parameter_map =
-      problem_impl.parameter_map();
   const map<int, set<double*> >& groups =
       ordering->group_id_to_parameter_blocks();
 
@@ -810,16 +846,12 @@
 // Reorder the residuals for program, if necessary, so that the residuals
 // involving each E block occur together. This is a necessary condition for the
 // Schur eliminator, which works on these "row blocks" in the jacobian.
-bool SolverImpl::MaybeReorderResidualBlocks(const Solver::Options& options,
-                                            Program* program,
-                                            string* error) {
-  // Only Schur types require the lexicographic reordering.
-  if (!IsSchurType(options.linear_solver_type)) {
-    return true;
-  }
-
-  const int num_eliminate_blocks =
-      options.ordering->group_id_to_parameter_blocks().begin()->second.size();
+bool SolverImpl::LexicographicallyOrderResidualBlocks(const int num_eliminate_blocks,
+                                                      Program* program,
+                                                      string* error) {
+  CHECK_GE(num_eliminate_blocks, 1)
+      << "Congratulations, you found a Ceres bug! Please report this error "
+      << "to the developers.";
 
   // Create a histogram of the number of residuals for each E block. There is an
   // extra bucket at the end to catch all non-eliminated F blocks.
@@ -894,16 +926,16 @@
 }
 
 Evaluator* SolverImpl::CreateEvaluator(const Solver::Options& options,
+                                       const ProblemImpl::ParameterMap& parameter_map,
                                        Program* program,
                                        string* error) {
   Evaluator::Options evaluator_options;
   evaluator_options.linear_solver_type = options.linear_solver_type;
-
   evaluator_options.num_eliminate_blocks =
       (options.ordering->NumGroups() > 0 &&
        IsSchurType(options.linear_solver_type))
-       ? options.ordering->group_id_to_parameter_blocks().begin()->second.size()
-       : 0;
+      ? options.ordering->group_id_to_parameter_blocks().begin()->second.size()
+      : 0;
   evaluator_options.num_threads = options.num_threads;
   return Evaluator::Create(evaluator_options, program, error);
 }
diff --git a/internal/ceres/solver_impl.h b/internal/ceres/solver_impl.h
index 076a371..eb81696 100644
--- a/internal/ceres/solver_impl.h
+++ b/internal/ceres/solver_impl.h
@@ -35,6 +35,7 @@
 #include <vector>
 #include "ceres/internal/port.h"
 #include "ceres/solver.h"
+#include "ceres/problem_impl.h"
 
 namespace ceres {
 class Ordering;
@@ -43,7 +44,7 @@
 
 class Evaluator;
 class LinearSolver;
-class ProblemImpl;
+class InnerIterationMinimizer;
 class Program;
 
 class SolverImpl {
@@ -58,6 +59,7 @@
   // and residuals eliminated, and in the case of automatic schur
   // ordering, has the E blocks first in the resulting program, with
   // options.num_eliminate_blocks set appropriately.
+  //
   // If fixed_cost is not NULL, the residual blocks that are removed
   // are evaluated and the sum of their cost is returned in fixed_cost.
   static Program* CreateReducedProgram(Solver::Options* options,
@@ -73,31 +75,35 @@
   static LinearSolver* CreateLinearSolver(Solver::Options* options,
                                           string* error);
 
-  // Reorder the parameter blocks in program using the vector
-  // ordering. A return value of true indicates success and false
-  // indicates an error was encountered whose cause is logged to
-  // LOG(ERROR).
-  static bool ApplyUserOrdering(const ProblemImpl& problem_impl,
+  // Reorder the parameter blocks in program using the ordering. A
+  // return value of true indicates success and false indicates an
+  // error was encountered whose cause is logged to LOG(ERROR).
+  static bool ApplyUserOrdering(const ProblemImpl::ParameterMap& parameter_map,
                                 const Ordering* ordering,
                                 Program* program,
                                 string* error);
 
+
   // Reorder the residuals for program, if necessary, so that the
-  // residuals involving each E block occur together. This is a
-  // necessary condition for the Schur eliminator, which works on
-  // these "row blocks" in the jacobian.
-  static bool MaybeReorderResidualBlocks(const Solver::Options& options,
-                                         Program* program,
-                                         string* error);
+  // residuals involving e block (i.e., the first num_eliminate_block
+  // parameter blocks) occur together. This is a necessary condition
+  // for the Schur eliminator as well as the InnerIterationMinimizer.
+  static bool LexicographicallyOrderResidualBlocks(
+      const int num_eliminate_blocks,
+      Program* program,
+      string* error);
 
   // Create the appropriate evaluator for the transformed program.
-  static Evaluator* CreateEvaluator(const Solver::Options& options,
-                                    Program* program,
-                                    string* error);
+  static Evaluator* CreateEvaluator(
+      const Solver::Options& options,
+      const ProblemImpl::ParameterMap& parameter_map,
+      Program* program,
+      string* error);
 
   // Run the minimization for the given evaluator and configuration.
   static void Minimize(const Solver::Options &options,
                        Program* program,
+                       InnerIterationMinimizer* inner_iteration_minimizer,
                        Evaluator* evaluator,
                        LinearSolver* linear_solver,
                        double* parameters,
@@ -106,9 +112,9 @@
   // Remove the fixed or unused parameter blocks and residuals
   // depending only on fixed parameters from the problem. Also updates
   // num_eliminate_blocks, since removed parameters changes the point
-  // at which the eliminated blocks is valid.
-  // If fixed_cost is not NULL, the residual blocks that are removed
-  // are evaluated and the sum of their cost is returned in fixed_cost.
+  // at which the eliminated blocks is valid.  If fixed_cost is not
+  // NULL, the residual blocks that are removed are evaluated and the
+  // sum of their cost is returned in fixed_cost.
   static bool RemoveFixedBlocksFromProgram(Program* program,
                                            Ordering* ordering,
                                            double* fixed_cost,
@@ -117,6 +123,10 @@
   static bool IsOrderingValid(const Solver::Options& options,
                               const ProblemImpl* problem_impl,
                               string* error);
+
+  static bool IsParameterBlockSetIndependent(
+      const set<double*> parameter_block_ptrs,
+      const vector<ResidualBlock*> residual_blocks);
 };
 
 }  // namespace internal
diff --git a/internal/ceres/solver_impl_test.cc b/internal/ceres/solver_impl_test.cc
index a19fca0..e612f8f 100644
--- a/internal/ceres/solver_impl_test.cc
+++ b/internal/ceres/solver_impl_test.cc
@@ -282,9 +282,10 @@
   options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
   string error;
 
-  EXPECT_TRUE(SolverImpl::MaybeReorderResidualBlocks(options,
-                                                     problem.mutable_program(),
-                                                     &error));
+  EXPECT_FALSE(SolverImpl::LexicographicallyOrderResidualBlocks(
+                   0,
+                   problem.mutable_program(),
+                   &error));
   EXPECT_EQ(current_residual_blocks.size(), residual_blocks.size());
   for (int i = 0; i < current_residual_blocks.size(); ++i) {
     EXPECT_EQ(current_residual_blocks[i], residual_blocks[i]);
@@ -337,9 +338,10 @@
   program->SetParameterOffsetsAndIndex();
 
   string error;
-  EXPECT_TRUE(SolverImpl::MaybeReorderResidualBlocks(options,
-                                                     problem.mutable_program(),
-                                                     &error));
+  EXPECT_TRUE(SolverImpl::LexicographicallyOrderResidualBlocks(
+                  2,
+                  problem.mutable_program(),
+                  &error));
   EXPECT_EQ(residual_blocks.size(), expected_residual_blocks.size());
   for (int i = 0; i < expected_residual_blocks.size(); ++i) {
     EXPECT_EQ(residual_blocks[i], expected_residual_blocks[i]);
@@ -407,9 +409,10 @@
   expected_residual_blocks.push_back(residual_blocks[3]);
   expected_residual_blocks.push_back(residual_blocks[2]);
 
-  EXPECT_TRUE(SolverImpl::MaybeReorderResidualBlocks(options,
-                                                     reduced_program.get(),
-                                                     &error));
+  EXPECT_TRUE(SolverImpl::LexicographicallyOrderResidualBlocks(
+                  2,
+                  reduced_program.get(),
+                  &error));
 
   EXPECT_EQ(reduced_program->residual_blocks().size(),
             expected_residual_blocks.size());
@@ -435,7 +438,7 @@
 
   Program program(problem.program());
   string error;
-  EXPECT_FALSE(SolverImpl::ApplyUserOrdering(problem,
+  EXPECT_FALSE(SolverImpl::ApplyUserOrdering(problem.parameter_map(),
                                              &ordering,
                                              &program,
                                              &error));
@@ -459,7 +462,7 @@
   Program* program = problem.mutable_program();
   string error;
 
-  EXPECT_TRUE(SolverImpl::ApplyUserOrdering(problem,
+  EXPECT_TRUE(SolverImpl::ApplyUserOrdering(problem.parameter_map(),
                                             &ordering,
                                             program,
                                             &error));
diff --git a/internal/ceres/trust_region_minimizer.cc b/internal/ceres/trust_region_minimizer.cc
index dd49f9e..b838b19 100644
--- a/internal/ceres/trust_region_minimizer.cc
+++ b/internal/ceres/trust_region_minimizer.cc
@@ -45,6 +45,7 @@
 #include "ceres/internal/scoped_ptr.h"
 #include "ceres/linear_least_squares_problems.h"
 #include "ceres/sparse_matrix.h"
+#include "ceres/stringprintf.h"
 #include "ceres/trust_region_strategy.h"
 #include "ceres/types.h"
 #include "ceres/wall_time.h"
@@ -102,8 +103,6 @@
   //
   // Both of these indicate that this is the wrong place for this
   // code, and going forward this should needs fixing/refactoring.
-  LOG(WARNING) << "Dumping linear least squares problem to disk is "
-               << "currently broken.";
   return true;
 }
 
@@ -142,7 +141,6 @@
   iteration_summary.iteration = 0;
   iteration_summary.step_is_valid = false;
   iteration_summary.step_is_successful = false;
-  iteration_summary.cost = summary->initial_cost;
   iteration_summary.cost_change = 0.0;
   iteration_summary.gradient_max_norm = 0.0;
   iteration_summary.step_norm = 0.0;
@@ -162,6 +160,8 @@
     return;
   }
 
+  iteration_summary.cost = cost + summary->fixed_cost;
+
   int num_consecutive_nonmonotonic_steps = 0;
   double minimum_cost = cost;
   double reference_cost = cost;
@@ -294,10 +294,12 @@
       if (++num_consecutive_invalid_steps >=
           options_.max_num_consecutive_invalid_steps) {
         summary->termination_type = NUMERICAL_FAILURE;
-        LOG(WARNING) << "Terminating. Number of successive invalid steps more "
-                     << "than "
-                     << "Solver::Options::max_num_consecutive_invalid_steps: "
-                     << options_.max_num_consecutive_invalid_steps;
+        summary->error = StringPrintf(
+            "Terminating. Number of successive invalid steps more "
+            "than Solver::Options::max_num_consecutive_invalid_steps: %d",
+            options_.max_num_consecutive_invalid_steps);
+
+        LOG(WARNING) << summary->error;
         return;
       }
 
@@ -306,7 +308,7 @@
       // as an unsuccessful iteration. Since the various callbacks are
       // still executed, we are going to fill the iteration summary
       // with data that assumes a step of length zero and no progress.
-      iteration_summary.cost = cost;
+      iteration_summary.cost = cost + summary->fixed_cost;
       iteration_summary.cost_change = 0.0;
       iteration_summary.gradient_max_norm =
           summary->iterations.back().gradient_max_norm;
@@ -319,7 +321,33 @@
 
       // Undo the Jacobian column scaling.
       delta = (trust_region_step.array() * scale.array()).matrix();
-      iteration_summary.step_norm = delta.norm();
+      if (!evaluator->Plus(x.data(), delta.data(), x_plus_delta.data())) {
+        summary->termination_type = NUMERICAL_FAILURE;
+        summary->error =
+            "Terminating. Failed to compute Plus(x, delta, x_plus_delta).";
+
+        LOG(WARNING) << summary->error;
+        return;
+      }
+
+      // Try this step.
+      double new_cost = numeric_limits<double>::max();
+      if (!evaluator->Evaluate(x_plus_delta.data(),
+                               &new_cost,
+                               NULL, NULL, NULL)) {
+        // If the evaluation of the new cost fails, treat it as a step
+        // with high cost.
+        LOG(WARNING) << "Step failed to evaluate. "
+                     << "Treating it as step with infinite cost";
+        new_cost = numeric_limits<double>::max();
+      } else if (new_cost < cost && options.inner_iteration_minimizer != NULL) {
+        Solver::Summary inner_iteration_summary;
+        options.inner_iteration_minimizer->Minimize(options,
+                                                    x_plus_delta.data(),
+                                                    &inner_iteration_summary);
+      }
+
+      iteration_summary.step_norm = (x - x_plus_delta).norm();
 
       // Convergence based on parameter_tolerance.
       const double step_size_tolerance =  options_.parameter_tolerance *
@@ -334,25 +362,6 @@
         return;
       }
 
-      if (!evaluator->Plus(x.data(), delta.data(), x_plus_delta.data())) {
-        summary->termination_type = NUMERICAL_FAILURE;
-        LOG(WARNING) << "Terminating. Failed to compute "
-                     << "Plus(x, delta, x_plus_delta).";
-        return;
-      }
-
-      // Try this step.
-      double new_cost;
-      if (!evaluator->Evaluate(x_plus_delta.data(),
-                               &new_cost,
-                               NULL, NULL, NULL)) {
-        // If the evaluation of the new cost fails, treat it as a step
-        // with high cost.
-        LOG(WARNING) << "Step failed to evaluate. "
-                     << "Treating it as step with infinite cost";
-        new_cost = numeric_limits<double>::max();
-      }
-
       VLOG(2) << "old cost: " << cost << " new cost: " << new_cost;
       iteration_summary.cost_change =  cost - new_cost;
       const double absolute_function_tolerance =
@@ -420,7 +429,8 @@
                                NULL,
                                jacobian)) {
         summary->termination_type = NUMERICAL_FAILURE;
-        LOG(WARNING) << "Terminating: Residual and Jacobian evaluation failed.";
+        summary->error = "Terminating: Residual and Jacobian evaluation failed.";
+        LOG(WARNING) << summary->error;
         return;
       }