I was trying to find results about the rate of convergence for the L-BFGS algorithm (in the nonlinear case).
What I end up with so far is that
- the BFGS-Algorithm converges Q-superlinearly
- this 50 year old Paper characterizing superlinear convergence of quasi-newton methods
- Theorem 3.5. (and 3.6.) in Nocedal's Numerical Optimization which do not give conditions that make sure the step length equals one for all but finitely many iterations.
Is there maybe a known negative result which I did not find?
Any help is appreciated, thank you in advance!