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# NP-Incompleteness

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## L-BFGS

04 Sep 2020

BFGS stands for Broyden–Fletcher–Goldfarb–Shanno algorithm [1] and it’s a non-linear numerical optimization method. L-BFGS means Low Memory BFGS and is a variant of the original algorithm that uses less memory [2]. The problem it’s aiming to solve is to mimize a given function $f: R^d \rightarrow R$ (this is applicable to a maximization problem - we just need to solve for $-f$).

In this post we’ll cover 5 topics: Taylor Expansion, Newton’s method, QuasiNewton methods, BFGS and L-BFGS. We then look back to see how all these fit together in the big picture.