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>
