Linear solvers for Levenberg-Marquardt

[徐维鹏]

Hi,

I'm using the Levenberg-Marquardt method to solve a nonlinear optimization problem. When I used SPARSE_NORMAL_CHOLESKY as the linear solver, I got this error: "Intel MKL ERROR: Parameter 4 was incorrect on entry to DPOTRF." But it's all right if I use CGNR. I also tried SPARSE_NORMAL_CHOLESKY with less parameter blocks, and it worked fine. So is this error due to that the problem is too large? If so, what is the limitation for SPARSE_NORMAL_CHOLESKY? Does CGNR yield the same accuracy as SPARSE_NORMAL_CHOLESKY?

Thanks.

Weipeng

[Sameer Agarwal]

Weipeng,
what sized problems are you solving?

Sameer

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[徐维鹏]

Hi Sameer,

I have 7k parameter blocks and 6k residual blocks. Here's the summary for reference.

Solver Summary (v 1.10.0-eigen-(3.2.0)-lapack-suitesparse-(4.2.1)-openmp)

                                     Original                  Reduced

Parameter blocks                         7068                     7068

Parameters                               7068                     7068

Residual blocks                          5890                     5890

Residual                                 8246                     8246

Minimizer                        TRUST_REGION

Trust region strategy     LEVENBERG_MARQUARDT

                                        Given                     Used

Linear solver                            CGNR                     CGNR

Preconditioner                         JACOBI                   JACOBI

Threads                                     8                        8

Linear solver threads                       8                        8

Cost:

Initial                          2.257673e+06

Final                            1.024263e+05

Change                           2.155247e+06

Minimizer iterations                       61

Successful steps                           61

Unsuccessful steps                          0

Time (in seconds):

Preprocessor                           0.0118

  Residual evaluation                  0.1117

    Line search cost evaluation        0.0000

  Jacobian evaluation                  0.8170

    Line search gradient evaluation    0.4995

  Linear solver                        1.0929

  Line search polynomial minimization  0.0007

Minimizer                              2.2211

Postprocessor                          0.0005

Total                                  2.2334

Termination:                      CONVERGENCE (Function tolerance reached. |cost_change|/cost: 7.715802e-07 <= 1.000000e-06)

>> 

在 2015年5月27日星期三 UTC+10下午2:47:12，Sameer Agarwal写道：