example of trivial optimization problem on 2-d circle for the purpose of comparison between ceres-solver and TensorFlow

trivial_opt_ceres.cpp

#include "ceres/ceres.h"
#include "glog/logging.h"

using ceres::CostFunction;
using ceres::AutoDiffCostFunction;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;

struct CostFunctor {
  template <typename T>
  bool operator()(const T* const x, T* residual) const {
    residual[0] = T(1.0) - cos(x[0]);
    residual[1] = T(1.0) - sin(x[0]);
    return true;
  }
};

int main(int argc, char** argv) {
  google::InitGoogleLogging(argv[0]);

  const double pi = 3.1415926535;

  double x[1] = {0};

  Problem problem;

  CostFunction* cost_function =
      new AutoDiffCostFunction<CostFunctor, 2, 1>(new CostFunctor);
  problem.AddResidualBlock(cost_function, NULL, x);

  Solver::Options options;
  options.minimizer_progress_to_stdout = true;
  Solver::Summary summary;
  Solve(options, &problem, &summary);

  std::cout << summary.BriefReport() << "\n";
  std::cout << "opt_x:" << x[0] << "\n";
  std::cout << "ans_x:" << pi/4 << "\n";

  return 0;
}

trivial_opt_tensorflow.py

import tensorflow as tf
import numpy as np

o = np.array([1,1])
theta = tf.Variable(tf.zeros([1]))
xy = tf.concat(0,[tf.cos(theta),tf.sin(theta)])

loss = tf.reduce_mean(tf.square(xy - o))
optimizer = tf.train.AdagradOptimizer(0.5)
train = optimizer.minimize(loss)

init = tf.initialize_all_variables()

sess = tf.Session()
sess.run(init)

for step in xrange(201):
    sess.run(train)
    if step % 20 == 0:
        print step, sess.run(theta)