|  | @@ -133,11 +133,12 @@ gives us
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				|  |  |  
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				|  |  |  .. code-block:: bash
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				|  |  |  
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				|  |  | -      0: f: 1.250000e+01 d: 0.00e+00 g: 5.00e+00 h: 0.00e+00 rho: 0.00e+00 mu: 1.00e+04 li:  0 it: 6.91e-06 tt: 1.91e-03
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				|  |  | -      1: f: 1.249750e-07 d: 1.25e+01 g: 5.00e-04 h: 5.00e+00 rho: 1.00e+00 mu: 3.00e+04 li:  1 it: 2.81e-05 tt: 1.99e-03
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				|  |  | -      2: f: 1.388518e-16 d: 1.25e-07 g: 1.67e-08 h: 5.00e-04 rho: 1.00e+00 mu: 9.00e+04 li:  1 it: 1.00e-05 tt: 2.01e-03
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				|  |  | -   Ceres Solver Report: Iterations: 2, Initial cost: 1.250000e+01, Final cost: 1.388518e-16, Termination: CONVERGENCE.
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				|  |  | -   x : 5 -> 10
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				|  |  | +   iter      cost      cost_change  |gradient|   |step|    tr_ratio  tr_radius  ls_iter  iter_time  total_time
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				|  |  | +      0  4.512500e+01    0.00e+00    9.50e+00   0.00e+00   0.00e+00  1.00e+04       0    5.33e-04    3.46e-03
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				|  |  | +      1  4.511598e-07    4.51e+01    9.50e-04   9.50e+00   1.00e+00  3.00e+04       1    5.00e-04    4.05e-03
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				|  |  | +      2  5.012552e-16    4.51e-07    3.17e-08   9.50e-04   1.00e+00  9.00e+04       1    1.60e-05    4.09e-03
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				|  |  | +   Ceres Solver Report: Iterations: 2, Initial cost: 4.512500e+01, Final cost: 5.012552e-16, Termination: CONVERGENCE
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				|  |  | +   x : 0.5 -> 10
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				|  |  |  
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				|  |  |  Starting from a :math:`x=5`, the solver in two iterations goes to 10
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				|  |  |  [#f2]_. The careful reader will note that this is a linear problem and
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				|  | @@ -373,21 +374,64 @@ gives us:
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				|  |  |  
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				|  |  |  .. code-block:: bash
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				|  |  |  
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				|  |  | - Initial x1 = 3, x2 = -1, x3 = 0, x4 = 1
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				|  |  | -    0: f: 1.075000e+02 d: 0.00e+00 g: 1.55e+02 h: 0.00e+00 rho: 0.00e+00 mu: 1.00e+04 li:  0 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    1: f: 5.036190e+00 d: 1.02e+02 g: 2.00e+01 h: 2.16e+00 rho: 9.53e-01 mu: 3.00e+04 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    2: f: 3.148168e-01 d: 4.72e+00 g: 2.50e+00 h: 6.23e-01 rho: 9.37e-01 mu: 9.00e+04 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    3: f: 1.967760e-02 d: 2.95e-01 g: 3.13e-01 h: 3.08e-01 rho: 9.37e-01 mu: 2.70e+05 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    4: f: 1.229900e-03 d: 1.84e-02 g: 3.91e-02 h: 1.54e-01 rho: 9.37e-01 mu: 8.10e+05 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    5: f: 7.687123e-05 d: 1.15e-03 g: 4.89e-03 h: 7.69e-02 rho: 9.37e-01 mu: 2.43e+06 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    6: f: 4.804625e-06 d: 7.21e-05 g: 6.11e-04 h: 3.85e-02 rho: 9.37e-01 mu: 7.29e+06 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    7: f: 3.003028e-07 d: 4.50e-06 g: 7.64e-05 h: 1.92e-02 rho: 9.37e-01 mu: 2.19e+07 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    8: f: 1.877006e-08 d: 2.82e-07 g: 9.54e-06 h: 9.62e-03 rho: 9.37e-01 mu: 6.56e+07 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    9: f: 1.173223e-09 d: 1.76e-08 g: 1.19e-06 h: 4.81e-03 rho: 9.37e-01 mu: 1.97e+08 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -   10: f: 7.333425e-11 d: 1.10e-09 g: 1.49e-07 h: 2.40e-03 rho: 9.37e-01 mu: 5.90e+08 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -   11: f: 4.584044e-12 d: 6.88e-11 g: 1.86e-08 h: 1.20e-03 rho: 9.37e-01 mu: 1.77e+09 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | - Ceres Solver Report: Iterations: 12, Initial cost: 1.075000e+02, Final cost: 4.584044e-12, Termination: CONVERGENCE.
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				|  |  | - Final x1 = 0.00116741, x2 = -0.000116741, x3 = 0.000190535, x4 = 0.000190535
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				|  |  | +    Initial x1 = 3, x2 = -1, x3 = 0, x4 = 1
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				|  |  | +    iter      cost      cost_change  |gradient|   |step|    tr_ratio  tr_radius  ls_iter  iter_time  total_time
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				|  |  | +       0  1.075000e+02    0.00e+00    1.55e+02   0.00e+00   0.00e+00  1.00e+04       0    4.95e-04    2.30e-03
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				|  |  | +       1  5.036190e+00    1.02e+02    2.00e+01   2.16e+00   9.53e-01  3.00e+04       1    4.39e-05    2.40e-03
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				|  |  | +       2  3.148168e-01    4.72e+00    2.50e+00   6.23e-01   9.37e-01  9.00e+04       1    9.06e-06    2.43e-03
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				|  |  | +       3  1.967760e-02    2.95e-01    3.13e-01   3.08e-01   9.37e-01  2.70e+05       1    8.11e-06    2.45e-03
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				|  |  | +       4  1.229900e-03    1.84e-02    3.91e-02   1.54e-01   9.37e-01  8.10e+05       1    6.91e-06    2.48e-03
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				|  |  | +       5  7.687123e-05    1.15e-03    4.89e-03   7.69e-02   9.37e-01  2.43e+06       1    7.87e-06    2.50e-03
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				|  |  | +       6  4.804625e-06    7.21e-05    6.11e-04   3.85e-02   9.37e-01  7.29e+06       1    5.96e-06    2.52e-03
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				|  |  | +       7  3.003028e-07    4.50e-06    7.64e-05   1.92e-02   9.37e-01  2.19e+07       1    5.96e-06    2.55e-03
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				|  |  | +       8  1.877006e-08    2.82e-07    9.54e-06   9.62e-03   9.37e-01  6.56e+07       1    5.96e-06    2.57e-03
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				|  |  | +       9  1.173223e-09    1.76e-08    1.19e-06   4.81e-03   9.37e-01  1.97e+08       1    7.87e-06    2.60e-03
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				|  |  | +      10  7.333425e-11    1.10e-09    1.49e-07   2.40e-03   9.37e-01  5.90e+08       1    6.20e-06    2.63e-03
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				|  |  | +      11  4.584044e-12    6.88e-11    1.86e-08   1.20e-03   9.37e-01  1.77e+09       1    6.91e-06    2.65e-03
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				|  |  | +      12  2.865573e-13    4.30e-12    2.33e-09   6.02e-04   9.37e-01  5.31e+09       1    5.96e-06    2.67e-03
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				|  |  | +      13  1.791438e-14    2.69e-13    2.91e-10   3.01e-04   9.37e-01  1.59e+10       1    7.15e-06    2.69e-03
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				|  |  | +
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				|  |  | +    Ceres Solver v1.10.0 Solve Report
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				|  |  | +    ----------------------------------
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				|  |  | +                                         Original                  Reduced
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				|  |  | +    Parameter blocks                            4                        4
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				|  |  | +    Parameters                                  4                        4
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				|  |  | +    Residual blocks                             4                        4
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				|  |  | +    Residual                                    4                        4
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				|  |  | +
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				|  |  | +    Minimizer                        TRUST_REGION
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				|  |  | +
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				|  |  | +    Dense linear algebra library            EIGEN
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				|  |  | +    Trust region strategy     LEVENBERG_MARQUARDT
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				|  |  | +
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				|  |  | +                                            Given                     Used
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				|  |  | +    Linear solver                        DENSE_QR                 DENSE_QR
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				|  |  | +    Threads                                     1                        1
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				|  |  | +    Linear solver threads                       1                        1
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				|  |  | +
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				|  |  | +    Cost:
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				|  |  | +    Initial                          1.075000e+02
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				|  |  | +    Final                            1.791438e-14
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				|  |  | +    Change                           1.075000e+02
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				|  |  | +
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				|  |  | +    Minimizer iterations                       14
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				|  |  | +    Successful steps                           14
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				|  |  | +    Unsuccessful steps                          0
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				|  |  | +
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				|  |  | +    Time (in seconds):
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				|  |  | +    Preprocessor                            0.002
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				|  |  | +
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				|  |  | +      Residual evaluation                   0.000
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				|  |  | +      Jacobian evaluation                   0.000
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				|  |  | +      Linear solver                         0.000
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				|  |  | +    Minimizer                               0.001
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				|  |  | +
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				|  |  | +    Postprocessor                           0.000
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				|  |  | +    Total                                   0.005
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				|  |  | +
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				|  |  | +    Termination:                      CONVERGENCE (Gradient tolerance reached. Gradient max norm: 3.642190e-11 <= 1.000000e-10)
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				|  |  | +
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				|  |  | +    Final x1 = 0.000292189, x2 = -2.92189e-05, x3 = 4.79511e-05, x4 = 4.79511e-05
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				|  |  |  
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				|  |  |  It is easy to see that the optimal solution to this problem is at
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				|  |  |  :math:`x_1=0, x_2=0, x_3=0, x_4=0` with an objective function value of
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				|  | @@ -461,24 +505,24 @@ gives us:
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				|  |  |  
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				|  |  |  .. code-block:: bash
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				|  |  |  
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				|  |  | -    0: f: 1.211734e+02 d: 0.00e+00 g: 3.61e+02 h: 0.00e+00 rho: 0.00e+00 mu: 1.00e+04 li:  0 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    1: f: 1.211734e+02 d:-2.21e+03 g: 3.61e+02 h: 7.52e-01 rho:-1.87e+01 mu: 5.00e+03 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    2: f: 1.211734e+02 d:-2.21e+03 g: 3.61e+02 h: 7.51e-01 rho:-1.86e+01 mu: 1.25e+03 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    3: f: 1.211734e+02 d:-2.19e+03 g: 3.61e+02 h: 7.48e-01 rho:-1.85e+01 mu: 1.56e+02 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    4: f: 1.211734e+02 d:-2.02e+03 g: 3.61e+02 h: 7.22e-01 rho:-1.70e+01 mu: 9.77e+00 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    5: f: 1.211734e+02 d:-7.34e+02 g: 3.61e+02 h: 5.78e-01 rho:-6.32e+00 mu: 3.05e-01 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    6: f: 3.306595e+01 d: 8.81e+01 g: 4.10e+02 h: 3.18e-01 rho: 1.37e+00 mu: 9.16e-01 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    7: f: 6.426770e+00 d: 2.66e+01 g: 1.81e+02 h: 1.29e-01 rho: 1.10e+00 mu: 2.75e+00 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    8: f: 3.344546e+00 d: 3.08e+00 g: 5.51e+01 h: 3.05e-02 rho: 1.03e+00 mu: 8.24e+00 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -    9: f: 1.987485e+00 d: 1.36e+00 g: 2.33e+01 h: 8.87e-02 rho: 9.94e-01 mu: 2.47e+01 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -   10: f: 1.211585e+00 d: 7.76e-01 g: 8.22e+00 h: 1.05e-01 rho: 9.89e-01 mu: 7.42e+01 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -   11: f: 1.063265e+00 d: 1.48e-01 g: 1.44e+00 h: 6.06e-02 rho: 9.97e-01 mu: 2.22e+02 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -   12: f: 1.056795e+00 d: 6.47e-03 g: 1.18e-01 h: 1.47e-02 rho: 1.00e+00 mu: 6.67e+02 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | -   13: f: 1.056751e+00 d: 4.39e-05 g: 3.79e-03 h: 1.28e-03 rho: 1.00e+00 mu: 2.00e+03 li:  1 it: 0.00e+00 tt: 0.00e+00
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				|  |  | - Ceres Solver Report: Iterations: 13, Initial cost: 1.211734e+02, Final cost: 1.056751e+00, Termination: CONVERGENCE.
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				|  |  | - Initial m: 0 c: 0
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				|  |  | - Final   m: 0.291861 c: 0.131439
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				|  |  | -
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				|  |  | +    iter      cost      cost_change  |gradient|   |step|    tr_ratio  tr_radius  ls_iter  iter_time  total_time
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				|  |  | +       0  1.211734e+02    0.00e+00    3.61e+02   0.00e+00   0.00e+00  1.00e+04       0    5.34e-04    2.56e-03
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				|  |  | +       1  1.211734e+02   -2.21e+03    0.00e+00   7.52e-01  -1.87e+01  5.00e+03       1    4.29e-05    3.25e-03
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				|  |  | +       2  1.211734e+02   -2.21e+03    0.00e+00   7.51e-01  -1.86e+01  1.25e+03       1    1.10e-05    3.28e-03
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				|  |  | +       3  1.211734e+02   -2.19e+03    0.00e+00   7.48e-01  -1.85e+01  1.56e+02       1    1.41e-05    3.31e-03
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				|  |  | +       4  1.211734e+02   -2.02e+03    0.00e+00   7.22e-01  -1.70e+01  9.77e+00       1    1.00e-05    3.34e-03
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				|  |  | +       5  1.211734e+02   -7.34e+02    0.00e+00   5.78e-01  -6.32e+00  3.05e-01       1    1.00e-05    3.36e-03
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				|  |  | +       6  3.306595e+01    8.81e+01    4.10e+02   3.18e-01   1.37e+00  9.16e-01       1    2.79e-05    3.41e-03
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				|  |  | +       7  6.426770e+00    2.66e+01    1.81e+02   1.29e-01   1.10e+00  2.75e+00       1    2.10e-05    3.45e-03
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				|  |  | +       8  3.344546e+00    3.08e+00    5.51e+01   3.05e-02   1.03e+00  8.24e+00       1    2.10e-05    3.48e-03
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				|  |  | +       9  1.987485e+00    1.36e+00    2.33e+01   8.87e-02   9.94e-01  2.47e+01       1    2.10e-05    3.52e-03
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				|  |  | +      10  1.211585e+00    7.76e-01    8.22e+00   1.05e-01   9.89e-01  7.42e+01       1    2.10e-05    3.56e-03
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				|  |  | +      11  1.063265e+00    1.48e-01    1.44e+00   6.06e-02   9.97e-01  2.22e+02       1    2.60e-05    3.61e-03
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				|  |  | +      12  1.056795e+00    6.47e-03    1.18e-01   1.47e-02   1.00e+00  6.67e+02       1    2.10e-05    3.64e-03
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				|  |  | +      13  1.056751e+00    4.39e-05    3.79e-03   1.28e-03   1.00e+00  2.00e+03       1    2.10e-05    3.68e-03
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				|  |  | +    Ceres Solver Report: Iterations: 13, Initial cost: 1.211734e+02, Final cost: 1.056751e+00, Termination: CONVERGENCE
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				|  |  | +    Initial m: 0 c: 0
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				|  |  | +    Final   m: 0.291861 c: 0.131439
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				|  |  |  
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				|  |  |  Starting from parameter values :math:`m = 0, c=0` with an initial
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				|  |  |  objective function value of :math:`121.173` Ceres finds a solution
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