[Ipopt-tickets] [Ipopt] #94: need a dense solver for small-scale optimization

[Ipopt]

#94: need a dense solver for small-scale optimization
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  Reporter:  klingenberg        |       Owner:  andreasw                                 
      Type:  enhancement        |      Status:  assigned                                 
  Priority:  normal             |   Component:  Ipopt                                    
   Version:  3.5 (C++ Version)  |    Severity:  normal                                   
Resolution:                     |    Keywords:  dense solver singular value decomposition
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Changes (by andreasw):

  * owner:  ipopt-team => andreasw
  * status:  new => assigned
  * version:  3.4 (C++ Version) => 3.5 (C++ Version)
  * type:  defect => enhancement

Comment:

 Hi,

 It would not be a trivial change to use dense matrices in the Ipopt code.
 One would have to change the data format in which the matrices are stored
 (currently they are stored in a triplet format, three data items (row
 index, column index, value) for each non-zero entry), and it would also
 require to change how the linear solver is called.  The changes would
 affect files in the src/LinAlg subdirectory.  And it then would also make
 sense to change the user interface to request derivative matrices directly
 in dense format, so a lot in src/Interfaces would also change.

 Ipopt is an interior point method and as such targeting large problems,
 with thousands and possibly millions of variables, and dense problems of
 that size are out of the question.

 The current sparse solvers are "accurate" in the sense that they solve the
 linear systems up to a high precision (close to machine precision) - they
 are based on a direct factorization of the matrices (and not on an
 iterative procedure which might produce less accurate solutions).  In
 terms of accuracy, I doubt that much would be gained from switching to a
 dense factorization (as in LAPACK) compared using the sparse linear
 solvers that are interfaced now.  In fact, some of the linear solvers
 (such as Pardiso) would just call LAPACK for the dense part in the
 matrices that they encounter.  The only advantage of using dense LAPACK
 routines directly would be speed.

 There might be other optimization code specifically for small-scale
 problems that are more suited for your application.

 Sorry this is not as helpful as you might have hoped.  I will close the
 ticket soon.

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Ticket URL: <https://projects.coin-or.org/Ipopt/ticket/94#comment:1>
Ipopt <http://projects.coin-or.org/Ipopt>
Interior-point optimizer for nonlinear programs.