[Insight-users] Why itk::LBFGSBOptimizer and itk::LBFGSOptimizer are classed as single-variant o

[Ali -]

I guess Stefan is right. There is no such thing as vnl_multiple_valued_cost_function, hence, itk::LBFGSBOptimizer and itk::LBFGSOptimizer shouldn't have been classified as single-variant optimisers in ITK and they should be modified for accepting itk::MultipleValuedCostFunction.


>Hi,


>The itk/vxl::LBFGS(B)Optimizer implementation IS multivariate. The
'multivariate' label refers to the number of variables (input arguments
of the cost function) over which is optimised. 


>the optimisaton problem is:

>min_x f(x)

>
On the site
http://www.alglib.net/optimization/ 
a multivariate optimisation method means that dim(x) >1 is
allowed.

>
The LBFGSOptimizer is not suitable for MultipleValuedCostFucnction, as
far as I know, only for SingleValuedCostFunctions.

>
singlevalued means: dim(f) = 1
>
multiplevalued means: dim(f) > 1

>
The vnl_cost_function indeed inherits from the vnl_unary_function, but
the vnl_unary_function is templated over a vector of doubles, which
contains the input argument x:

>
class vnl_cost_function : public vnl_unary_function<double,
vnl_vector<double> >

>
with kind regards,
>
stefan


> 
> 
> 
> Hi Ali,
> 
> 
> 1) It is not a "problem", it is an "implementation feature".   :-)
> 
> 
> 
> 2) It is not in ITK, it is in VXL,
> 
>     Please look at the implementation in the file:
> 
>          Insight/Utilities/vxl/core/vnl/vnl_lbfgs.h
> 
>     Where the optimizer takes as input a vnl_cost_function
>     object, that derives from the vnl_unary_function class.
> 
> 
> 
> 3) It will be great to have multi-variate implementations
>     of these optimizers. If you are motivated to write one,
>     it will make a great contribution to the Insight Journal.
> 
> 
> 
>      Regards,
> 
> 
>         Luis
> 
> 
> 
> -------------
> Ali - wrote:
> > Hi,
> > 
> > The VNL wrappers itk::LBFGSBOptimizer and itk::LBFGSOptimizer are 
> > classified as single-variant optimiser, while being based on the 
> > quasi-Newton method, they are multi-variant optimisers by nature -- see 
> > http://www.alglib.net/optimization/ . Is this the ITK wrapper problem or 
> > a VNL issue?
> > 
> > _______________________________________________
> > Insight-users mailing list
> > Insight-users at itk.org
> > http://www.itk.org/mailman/listinfo/insight-users

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