Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asymptotic convergence and acceleration of gradient methods   We consider the asymptotic behavior of a family of gradient methods, which
include the steepest descent and minimal gradient methods as special instances.
It is proved that each method in the family will asymptotically zigzag between
two directions. Asymptotic convergence results of the objective value, gradient
norm, and stepsize are presented as well. To accelerate the family of gradient
methods, we further exploit spectral properties of stepsizes to break the
zigzagging pattern. In particular, a new stepsize is derived by imposing finite
termination on minimizing two-dimensional strictly convex quadratic function.
It is shown that, for the general quadratic function, the proposed stepsize
asymptotically converges to the reciprocal of the largest eigenvalue of the
Hessian. Furthermore, based on this spectral property, we propose a periodic
gradient method by incorporating the Barzilai-Borwein method. Numerical
comparisons with some recent successful gradient methods show that our new
method is very promising.

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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex