Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A single potential governing convergence of conjugate gradient,
  accelerated gradient and geometric descent   Nesterov's accelerated gradient (AG) method for minimizing a smooth strongly
convex function $f$ is known to reduce $f({\bf x}_k)-f({\bf x}^*)$ by a factor
of $\epsilon\in(0,1)$ after $k=O(\sqrt{L/\ell}\log(1/\epsilon))$ iterations,
where $\ell,L$ are the two parameters of smooth strong convexity. Furthermore,
it is known that this is the best possible complexity in the function-gradient
oracle model of computation. Modulo a line search, the geometric descent (GD)
method of Bubeck, Lee and Singh has the same bound for this class of functions.
The method of linear conjugate gradients (CG) also satisfies the same
complexity bound in the special case of strongly convex quadratic functions,
but in this special case it can be faster than the AG and GD methods.
  Despite similarities in the algorithms and their asymptotic convergence
rates, the conventional analysis of the running time of CG is mostly disjoint
from that of AG and GD. The analyses of the AG and GD methods are also rather
distinct.
  Our main result is analyses of the three methods that share several common
threads: all three analyses show a relationship to a certain "idealized
algorithm", all three establish the convergence rate through the use of the
Bubeck-Lee-Singh geometric lemma, and all three have the same potential that is
computable at run-time and exhibits decrease by a factor of $1-\sqrt{\ell/L}$
or better per iteration.
  One application of these analyses is that they open the possibility of hybrid
or intermediate algorithms. One such algorithm is proposed herein and is shown
to perform well in computational tests.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci