ceres实现最优估计算法，C++分别实现牛顿法、高斯牛顿法，阻尼最小二乘法

以下是使用Ceres实现牛顿法、高斯牛顿法和阻尼最小二乘法的示例代码：

牛顿法：

#include <iostream>
#include "ceres/ceres.h"

using namespace std;

// 定义残差函数
struct CostFunctor {
    template <typename T>
    bool operator()(const T* const x, T* residual) const {
        residual[0] = T(10.0) - x[0];
        return true;
    }
};

int main(int argc, char** argv) {
    // 初始化问题
    ceres::Problem problem;

    // 添加变量
    double x = 0.5;
    problem.AddParameterBlock(&x, 1);

    // 添加残差项
    ceres::CostFunction* cost_function =
        new ceres::AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor);
    problem.AddResidualBlock(cost_function, nullptr, &x);

    // 设置求解选项
    ceres::Solver::Options options;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
    options.trust_region_strategy_type = ceres::LEVENBERG_MARQUARDT;

    // 求解问题
    ceres::Solver::Summary summary;
    ceres::Solve(options, &problem, &summary);

    // 输出结果
    cout << summary.BriefReport() << endl;
    cout << "x = " << x << endl;

    return 0;
}

高斯牛顿法：

#include <iostream>
#include "ceres/ceres.h"

using namespace std;

// 定义残差函数
struct CostFunctor {
    template <typename T>
    bool operator()(const T* const x, T* residual) const {
        residual[0] = T(10.0) - x[0];
        return true;
    }
};

int main(int argc, char** argv) {
    // 初始化问题
    ceres::Problem problem;

    // 添加变量
    double x = 0.5;
    problem.AddParameterBlock(&x, 1);

    // 添加残差项
    ceres::CostFunction* cost_function =
        new ceres::AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor);
    problem.AddResidualBlock(cost_function, nullptr, &x);

    // 设置求解选项
    ceres::Solver::Options options;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
    options.trust_region_strategy_type = ceres::DOGLEG;

    // 求解问题
    ceres::Solver::Summary summary;
    ceres::Solve(options, &problem, &summary);

    // 输出结果
    cout << summary.BriefReport() << endl;
    cout << "x = " << x << endl;

    return 0;
}

阻尼最小二乘法：

#include <iostream>
#include "ceres/ceres.h"

using namespace std;

// 定义残差函数
struct CostFunctor {
    template <typename T>
    bool operator()(const T* const x, T* residual) const {
        residual[0] = T(10.0) - x[0];
        return true;
    }
};

int main(int argc, char** argv) {
    // 初始化问题
    ceres::Problem problem;

    // 添加变量
    double x = 0.5;
    problem.AddParameterBlock(&x, 1);

    // 添加残差项
    ceres::CostFunction* cost_function =
        new ceres::AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor);
    problem.AddResidualBlock(cost_function, nullptr, &x);

    // 设置求解选项
    ceres::Solver::Options options;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
    options.trust_region_strategy_type = ceres::DOGLEG;
    options.dogleg_type = ceres::SUBSPACE_DOGLEG;
    options.use_nonmonotonic_steps = true;

    // 求解问题
    ceres::Solver::Summary summary;
    ceres::Solve(options, &problem, &summary);

    // 输出结果
    cout << summary.BriefReport() << endl;
    cout << "x = " << x << endl;

    return 0;
}

在这些示例中，我们将牛顿法、高斯牛顿法和阻尼最小二乘法的求解选项分别设置为LEVENBERG_MARQUARDT、DOGLEG和SUBSPACE_DOGLEG，并使用ceres::Solve函数求解问题。最后，我们输出求解结果。