Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iteration-complexity of first-order augmented Lagrangian methods for
  convex conic programming   In this paper we consider a class of convex conic programming. In particular,
we propose an inexact augmented Lagrangian (I-AL) method for solving this
problem, in which the augmented Lagrangian subproblems are solved approximately
by a variant of Nesterov's optimal first-order method. We show that the total
number of first-order iterations of the proposed I-AL method for computing an
$\epsilon$-KKT solution is at most $\mathcal{O}(\epsilon^{-7/4})$. We also
propose a modified I-AL method and show that it has an improved
iteration-complexity $\mathcal{O}(\epsilon^{-1}\log\epsilon^{-1})$, which is so
far the lowest complexity bound among all first-order I-AL type of methods for
computing an $\epsilon$-KKT solution. Our complexity analysis of the I-AL
methods is mainly based on an analysis on inexact proximal point algorithm
(PPA) and the link between the I-AL methods and inexact PPA. It is
substantially different from the existing complexity analyses of the
first-order I-AL methods in the literature, which typically regard the I-AL
methods as an inexact dual gradient method. Compared to the mostly related I-AL
methods \cite{Lan16}, our modified I-AL method is more practically efficient
and also applicable to a broader class of problems.

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin