Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convergence of BFGS on a class of piecewise linear non-smooth
  functions   The quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method has proven to
be very reliable and efficient for the minimization of smooth objective
functions since its inception in the 1960s. Recently, it was observed
empirically that it also works remarkably well for non-smooth problems when
combined with the Armijo-Wolfe line search, but only very limited theoretical
convergence theory could be established so far. In this paper, we expand these
results by considering convex piecewise linear functions with two pieces that
are not bounded below. We prove that the algorithm always terminates in a
finite number of iterations, eventually generating an unbounded direction. In
other words, in contrast to the gradient method, the BFGS algorithm does not
converge to a non-stationary point.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
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The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex