[petsc-users] Linesearch algorithm

[Jed Brown]

On Tue, May 15, 2012 at 2:26 PM, behzad baghapour <
behzad.baghapour at gmail.com> wrote:

> OK. The (pseudo) transient technique is a way of globalizing the local
> convergent Newton methods which is very helpful when dealing with high
> nonlinear problems with a pure initial guess. But the classical line-search
> method is to minimize the problem 0.5IIR(x)II^2 which basically does not
> see the transient phase.


1. The transient term may give you a direction that is not a descent
direction for ||R(x)||^2. For such problems, you _must_ allow ||R(x)|| to
_increase_ before you can reach a steady state.

2. ||R(x)||^2 may not be a good objective functional for the line search,
especially for non-convex problems.


> Then I have to discard this phase in order to match with the structure of
> the method. So I am looking forward to find a way to tell the SNES to
> consider just the term: dR/dQ when using it to modify the search direction
> with its quadratic or cubic model.


The line search does not change the search direction, it changes the step
length.
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