使用谷神星优化多维函数

Optimising multi-dimensional functions with Ceres

本文关键字：函数 优化      更新时间：2023-10-16

我想使用谷神星来优化n个参数的函数。如何找到这个函数的梯度尚不清楚，尽管我确实有一个明确的成本。到目前为止，我一直在使用带有数字差异的 GSL，但我想我会尝试使用带有自动差异的 Ceres。

我看过玩具示例 helloworld_analytic_diff.cc，其中他们使用 AutoDiff 来最小化函数 f(x( = 0.5 (10 - x(^2 并阅读了教程，所以我想我会尝试将其扩展到二维函数 f(x，y( = (10-x(^2 +(20- y(^2，它的全局最小值为 x， y = 10， 20。但我有点卡在这个上面：

#include "ceres/ceres.h"
#include "glog/logging.h"
using ceres::AutoDiffCostFunction;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;

struct CostFunctor {
template <typename T> bool operator()(const T* const x, T* residual) const {
const T x1 = x[0];
const T y1 = x[1];
residual[0] = (10.0-x[0]) + (20.0-x[1]);
return true;
}
};
int main(int argc, char** argv) {
google::InitGoogleLogging(argv[0]);
double x[2] = {0.5, -3.0};
const double initial_x[2] = {0.5, -3.0};
Problem problem;
CostFunction* cost_function = new AutoDiffCostFunction<CostFunctor, 1, 2>(new CostFunctor);
problem.AddResidualBlock(cost_function, NULL, &x[0]);
// Run the solver!
Solver::Options options;
options.minimizer_progress_to_stdout = true;
Solver::Summary summary;
Solve(options, &problem, &summary);
std::cout << summary.BriefReport() << "n";
std::cout << "x : " << initial_x[0] << ", " << initial_x[0]
<< " -> " << x[0] << ", " << x[1]<< "n";
return 0;
}

但是，如果我运行它，它最终会收敛到不正确的内容，具体取决于最初的猜测：

Ceres Solver Report: Iterations: 3, Initial cost: 5.281250e+02, Final cost: 3.667046e-16, Termination: CONVERGENCE
x : 0.5, 0.5 -> 16.75, 13.25

关于我在这里做错了什么有什么想法吗？ 非常感谢！

您的成本函子是错误的。 您正在解决的优化问题是

[(10.0-x( + (20.0-y(]^2

而不是

(10-x(^2 +(20- y(^2，

这里应该做的是有两个成本函子，如下所示：

struct CostFunctor1 {
template <typename T> bool operator()(const T* const x, T* residual) const {
residual[0] = 10.0-x[0];
return true;
}
};
struct CostFunctor2 {
template <typename T> bool operator()(const T* const x, T* residual) const {
residual[0] = 20.0-x[1];
return true;
}
};
int main(int argc, char** argv) {
google::InitGoogleLogging(argv[0]);
double x[2] = {0.5, -3.0};
const double initial_x[2] = {0.5, -3.0};
Problem problem;
problem.AddResidualBlock(new AutoDiffCostFunction<CostFunctor1, 1, 2>(new 
CostFunctor1), NULL, &x[0]);
problem.AddResidualBlock(new AutoDiffCostFunction<CostFunctor2, 1, 2>(new 
CostFunctor2), NULL, &x[0]);
// Run the solver!
Solver::Options options;
options.minimizer_progress_to_stdout = true;
Solver::Summary summary;
Solve(options, &problem, &summary);
std::cout << summary.BriefReport() << "n";
std::cout << "x : " << initial_x[0] << ", " << initial_x[0]
<< " -> " << x[0] << ", " << x[1]<< "n";
return 0;
}
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