<div class="gmail_quote">On Tue, May 15, 2012 at 2:26 PM, behzad baghapour <span dir="ltr"><<a href="mailto:behzad.baghapour@gmail.com" target="_blank">behzad.baghapour@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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.</blockquote>
<div><br></div><div>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.</div><div>
<br></div><div>2. ||R(x)||^2 may not be a good objective functional for the line search, especially for non-convex problems.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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.</blockquote>
</div><br><div>The line search does not change the search direction, it changes the step length.</div>