How to use ceres-solver to solve high dimensional non-linear problem? - c++

Question

     I need to solve the optimization problem: . A and b are known. I use Zero to represent A and b to facilate the expression in the following code. The error is caused by problem.AddResidualBlock(cost_function, nullptr, &X); because the third argument needs to be double type and X is a vector with 50 elements. Can you give me some advice?
#include <cmath>
#include <ceres/ceres.h>
#include <Eigen/Core>
#include <Eigen/Eigen>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/StdVector>
#define PhaseNums 25
using namespace std;
using namespace ceres;
using namespace Eigen;
struct GammaResidual
{
GammaResidual(const MatrixXf A, const VectorXf b) : A_(A), b_(b) {}
template <typename T>
bool operator()(const T* const x, T* residual) const {
residual[0] = (A_ * x[0] - b_).transpose() * (A_ * x[0] - b_);
return true;
}
private:
const MatrixXf A_;
const VectorXf b_;
};
int main()
{
MatrixXf A = MatrixXf::Zero(2 * PhaseNums, 2 * PhaseNums);
VectorXf b = VectorXf::Zero(2 * PhaseNums);
VectorXf X = VectorXf::Zero(2 * PhaseNums);
Problem problem;
CostFunction* cost_function = new AutoDiffCostFunction<GammaResidual, 1, 1>(
new GammaResidual(A, b));
problem.AddResidualBlock(cost_function, nullptr, &X);
ceres::Solver::Options options;
options.minimizer_progress_to_stdout = true;
ceres::Solver::Summary summary;
ceres::Solve(options, &problem, &summary);
cout << summary.BriefReport() << endl;
}

Answer 1

I guess that If your X is a vector, you need to loop through it and add a residual a residual block for each x. Makes sense?