I think that this page should explain the Wolfe conditions a bit more. Now it states the conditions, but it does not explain what they imply.
- Good idea. I tried to add some header information so that a reader might have some idea what was going on. PDBailey (talk) 02:18, 21 November 2009 (UTC)
I believe that the inequality on the sign of the curvature condition (weak form) is backwards. Can someone take a look at this? 4 February 2010 —Preceding unsigned comment added by 18.104.22.168 (talk) 21:36, 4 February 2010 (UTC)
The link to the Goldstein conditions currently redirects back to the wolfe article itself. Should this point to a new page or a subsection within the wolfe conditions somewhere? Sim (talk) 06:57, 23 May 2010 (UTC)
Could someone please make a seperate article on the Goldstein Conditions. Summarized as follows:
f(x) + (1-c)(α)*(g^T*p) <= f(x+αp) <= f(x) + cα(g^T*p) : 0 < c < 1/2 p is the step direction, g is the gradient, g^T*p is the dot product of g and p; note, no index is used, but each variable could have "k" attached to indicate they are all on the same kth step.
Also note in both articles: The Wolfe conditions are better for Quasi-Newtons methods while the Goldstein conditions are better for exact Newton methods. In practice, the Goldstein conditions may actually find no suitable α; but in general, they have the same theoretic convergence properties.
Source: http://books.google.co.uk/books?id=epc5fX0lqRIC&pg=PA37&lpg=PA37&dq=wolfe+conditions&source=bl&ots=a9BCwHB3cA&sig=OAv0l7RGAmC_NvIv__yzSM5r3do&hl=en&ei=haHcTqH9HsvHtAad5czeCw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDoQ6AEwAw#v=onepage&q=wolfe%20conditions&f=false — Preceding unsigned comment added by Brydustin (talk • contribs) 11:08, 5 December 2011 (UTC)