Line search question

[Ryan Yan]

Hi Barry,
Thank you very much for the clarification and comment. The  p_n. J'. f_n
makes perfect sense.

Yan

On Sun, Dec 6, 2009 at 12:54 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> 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
>>>
>>
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20091206/b539259c/attachment.htm>