Github user jkbradley commented on a diff in the pull request:
https://github.com/apache/spark/pull/13262#discussion_r64252055
--- Diff: docs/ml-advanced.md ---
@@ -4,10 +4,85 @@ title: Advanced topics - spark.ml
displayTitle: Advanced topics - spark.ml
---
-# Optimization of linear methods
+* Table of contents
+{:toc}
+
+`\[
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+\]`
+
+# Optimization of linear methods (developer)
+
+## Limited-memory BFGS (L-BFGS)
+[L-BFGS](http://en.wikipedia.org/wiki/Limited-memory_BFGS) is an
optimization
+algorithm in the family of quasi-Newton methods to solve the optimization
problems of the form
+`$\min_{\wv \in\R^d} \; f(\wv)$`. The L-BFGS method approximates the
objective function locally as a
+quadratic without evaluating the second partial derivatives of the
objective function to construct the
+Hessian matrix. The Hessian matrix is approximated by previous gradient
evaluations, so there is no
+vertical scalability issue (the number of training features) when
computing the Hessian matrix
--- End diff --
"when computing" ---> "unlike computing"
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