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ceres-solver / ceres-solver

A large scale non-linear optimization library

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the gradient remains unchanged resulting in “Minimum trust region radius reached”

zdongchen opened this issue · comments

commented

I am looking for the value of the parameter when the function takes the minimum value. The function form is as $f=\Sigma(p_0+p_1x+p_2x^2+p_3x^3+p_4x^4)$ in which $x=c_0x_0+c_1x_1+c_2x_2+...$,the number of parameters is determined by the coefficient array, below is my implementation code, and the FullReport shows that the gradient is a constant value, and the trust region radius becomes smaller and smaller until it reaches the threshold, which results in the parameters not being updated, and they are still the initial values.

CostFunction::CostFunction(std::vector<std::vector<double>>& p, std::vector<std::vector<double>>& c, int num_x) : p_(p), c_(c), num_x_(num_x) {}

template <typename T>
bool CostFunction::operator()(const T* const* parameters, T* residual) const {
    T z = T(0.0);
    for(int i = 0; i < p_.size(); ++i) {
        T z_i = T(0.0);
        T x_sum = T(0.0);
        for(int j = 0; j < num_x_; ++j) {
            x_sum += c_[i][j] * parameters[0][j];
        }

        z_i += p_[i][0] + p_[i][1] * x_sum + p_[i][2] * pow(x_sum, 2) + p_[i][3] * pow(x_sum, 3) + p_[i][4] * pow(x_sum, 4);
        z += z_i;
    }

    residual[0] = z;
    return true;
}

void Solver(std::vector<std::vector<double>>& p, std::vector<std::vector<double>>& c, const int num_params) {
    double x[num_params];
    for(int i = 0; i < num_params; ++i) {
        x[i] = 0.5;
    }
    ceres::Problem* problem = new ceres::Problem;
    
    CostFunction* cost_function = new CostFunction(p, c, num_params);
    ceres::DynamicAutoDiffCostFunction<CostFunction, 4> dynamic_cost_function(cost_function);
    dynamic_cost_function.AddParameterBlock(1);
    dynamic_cost_function.SetNumResiduals(1);
    problem->AddResidualBlock(&dynamic_cost_function, nullptr, x);

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

    std::cout << summary.FullReport() << std::endl;
    for(int i = 0; i < num_params; ++i) {
        std::cout << "x[" << i << "] = " << x[i] << std::endl;
    }
}

the FullReport

iter      cost      cost_change  |gradient|   |step|    tr_ratio  tr_radius  ls_iter  iter_time  total_time
   0  1.057330e+04    0.00e+00    3.40e+01   0.00e+00   0.00e+00  1.00e+04        0    3.62e-04    6.05e-04
   1  1.635421e+05   -1.53e+05    3.40e+01   0.00e+00  -4.22e+03  5.00e+03        1    1.83e-04    9.05e-04
   2  1.635420e+05   -1.53e+05    3.40e+01   0.00e+00  -4.22e+03  1.25e+03        1    9.20e-05    1.36e-03
   3  1.635420e+05   -1.53e+05    3.40e+01   0.00e+00  -4.22e+03  1.56e+02        1    3.41e-05    1.51e-03
   4  1.635418e+05   -1.53e+05    3.40e+01   0.00e+00  -4.22e+03  9.77e+00        1    1.20e-04    2.02e-03
   5  1.635383e+05   -1.53e+05    3.40e+01   0.00e+00  -4.26e+03  3.05e-01        1    3.70e-05    2.18e-03
   6  1.635414e+05   -1.53e+05    3.40e+01   0.00e+00  -1.02e+04  4.77e-03        1    2.19e-05    2.25e-03
   7  1.635547e+05   -1.53e+05    3.40e+01   0.00e+00  -4.46e+05  3.73e-05        1    3.10e-05    2.37e-03
   8  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -5.67e+07  1.46e-07        1    1.88e-05    2.42e-03
   9  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -1.45e+10  2.84e-10        1    3.10e-05    2.53e-03
  10  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -7.43e+12  2.78e-13        1    2.10e-05    2.58e-03
  11  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -7.61e+15  1.36e-16        1    4.22e-05    2.76e-03
  12  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -1.56e+19  3.31e-20        1    1.50e-04    3.03e-03
  13  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -6.38e+22  4.04e-24        1    2.91e-05    3.14e-03
  14  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -5.23e+26  2.47e-28        1    2.10e-05    3.19e-03
  15  1.635551e+05   -1.53e+05    3.40e+01   0.00e+00  -8.57e+30  7.52e-33        1    6.99e-05    3.35e-03

Solver Summary (v 2.2.0-eigen-(3.4.0)-no_lapack-eigensparse)

                                     Original                  Reduced
Parameter blocks                            1                        1
Parameters                                  1                        1
Residual blocks                             7                        7
Residuals                                   7                        7

Minimizer                        TRUST_REGION
Trust region strategy     LEVENBERG_MARQUARDT
Sparse linear algebra library    EIGEN_SPARSE 

                                        Given                     Used
Linear solver          SPARSE_NORMAL_CHOLESKY   SPARSE_NORMAL_CHOLESKY
Threads                                     1                        1
Linear solver ordering              AUTOMATIC                        1

Cost:
Initial                          1.057330e+04
Final                            1.057330e+04
Change                           0.000000e+00

Minimizer iterations                       16
Successful steps                            1
Unsuccessful steps                         15

Time (in seconds):
Preprocessor                         0.000243

  Residual only evaluation           0.000278 (15)
  Jacobian & residual evaluation     0.000344 (1)
  Linear solver                      0.000483 (15)
Minimizer                            0.003446

Postprocessor                        0.000016
Total                                0.003706

Termination:                      CONVERGENCE (Minimum trust region radius reached. Trust region radius: 7.523164e-33 <= 1.000000e-32)

x[0] = 0.5
x[1] = 0.5
x[2] = 0.5
x[3] = 0.5
x[4] = 0.5
x[5] = 0.5
x[6] = 0.5

btw, the coefficient arrays p and c are as follows

c = [[0,0,0,0,0,-35,-32],
[0,0,0,33,0,0,0],
[0,0,0,-33,0,0,0],
[0,-29,0,0,-29,0,0],
[22,0,27,0,0,35,32],
[0,29,0,0,29,0,32],
[-22,0,-27,0,0,0,0]]

p = [[65.7746,0.240377,0.000291566,4.82587e-08,-8.01918e-11],
[55.2469,0.222333,0.000289126,5.64903e-08,-8.01918e-11],
[85.0069,0.261409,0.00026811,3.31716e-08,-8.01918e-11],
[65.7746,0.240377,0.000291566,4.82587e-08,-8.01918e-11],
[21.3355,0.108407,0.000191211,8.61348e-08,-8.01918e-11],
[29.7129,0.14492,0.00022873,7.87325e-08,-8.01918e-11],
[30.3014,0.147334,0.000231105,7.81974e-08,-8.01918e-11]]
commented

hi, why this is closed, so what does the message " (Minimum trust region radius reached. Trust region radius: 7.523164e-33 <= 1.000000e-32) " means, and is it a good solve result.