c++如何使用Ceres Solver解决优化问题_c++ Google的非线性优化库

find_package(Ceres REQUIRED)
target_link_libraries(your_program ${CERES_LIBRARIES})
target_include_directories(your_program PRIVATE ${CERES_INCLUDE_DIRS})

struct ExponentialResidual {
  ExponentialResidual(double x, double y) : x_(x), y_(y) {}
<p>template <typename T>
bool operator()(const T<em> parameters, T</em> residuals) const {
T a = parameters[0];
T b = parameters[1];
T c = parameters[2];
residuals[0] = T(y<em>) - ceres::exp(a * x</em> <em> x_ + b </em> x_ + c);
return true;
}</p><p>double x<em>, y</em>;
};

int main() {
  // 真实参数
  double a_true = 0.5, b_true = -1.0, c_true = 0.3;
  // 初始估计值
  double parameters[3] = {0.0, 0.0, 0.0};
<p>ceres::Problem problem;</p><p>// 生成模拟数据
for (double x = -1.0; x <= 1.0; x += 0.1) {
double y = exp(a_true <em> x </em> x + b_true <em> x + c_true);
// 添加噪声
y += 0.01 </em> rand() / RAND_MAX;</p><pre class="brush:php;toolbar:false;">// 创建代价函数，使用自动微分
ceres::CostFunction* cost_function =
    new ceres::AutoDiffCostFunction<ExponentialResidual, 1, 3>(
        new ExponentialResidual(x, y));

problem.AddResidualBlock(cost_function, nullptr, parameters);

  ceres::Solver::Options options;
  options.linear_solver_type = ceres::DENSE_QR;
  options.minimizer_progress_to_stdout = true;
<p>ceres::Solver::Summary summary;
ceres::Solve(options, &problem, &summary);</p><p>std::cout << summary.BriefReport() << "\n";
std::cout << "Estimated a: " << parameters[0] << "\n";
std::cout << "Estimated b: " << parameters[1] << "\n";
std::cout << "Estimated c: " << parameters[2] << "\n";</p><p>return 0;
}

problem.AddResidualBlock(cost_function,
                        new ceres::HuberLoss(1.0),
                        parameters);