LBFGS

[Jahanzaib]

Dear Expert
I have studied the LBFGS algorithms and found that during optimization it follow the following steps
•   Minimizing Forces
•   Compute the gradient
•   Update the search directions
•   Line search
•   Update the variables and memory history   
•   Check convergences

I am still confused about LBFGS the how this step could be explain mathematically, Expert please guide me a bit

[Anders Blom]

Maybe you already checked it out, but both https://en.wikipedia.org/wiki/Limited-memory_BFGS and https://stats.stackexchange.com/questions/284712/how-does-the-l-bfgs-work are very relevant. We use the Quasi-Newton approach, of course, snice we don't know the exact Hessian.