Line search question

[Barry Smith]

On Dec 6, 2009, at 11:43 AM, Barry Smith wrote:

>
>   I think the confusion comes from the fact that the Amijo condition  
> is almost always in the literature for minimization; not for  
> nonlinear equations.
>
> If we minimize F(x) the condition is F(x + alpha p) <= F(x) + c  
> alpha p' grad F(x) with c near 1.   Here ' denotes transpose
>
> For the PETSc nonlinear solver F(x) = .5 f(x)' f(x). Ok, now just  
> compute grad F in this case and the Jacobian pops right out. grad  
> F(x) = J f

      Correction;  it is actually       grad F(x) = J'f  hence in the  
code it computes f' (J p) so it does not need to apply J'

    Barry

>
> Hmm, looks like the comment is wrong where it says f_n . J . f_n, it  
> should say p_n. J. f_n
>
>   Barry
>
>
> On Dec 5, 2009, at 10:24 PM, Ryan Yan wrote:
>
>> Hi All,
>> I am trying to figure out how the line search is actually working  
>> in PETSc and I am looking at this link,
>>
>> http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/SNES/SNESLineSearchGetParams.html
>> F(x
>> Can anyone help to explain why there is a J in the amijo condition?
>>
>> alpha - The scalar such that .5*f_{n+1} . f_{n+1} <= .5*f_n . f_n -  
>> alpha |f_n . J . f_n|
>>
>>
>> Considering the fact that the newton direction p_n provide a J^{-1}  
>> and the gradient of the merit function( 1/2 f . f) provide a J,  
>> isn't correct to get rid of J in the definition above?
>>
>> Thanks for any suggestions,
>>
>> Yan
>