Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accelerated-gradient-based generalized Levenberg--Marquardt method with
  oracle complexity bound and local quadratic convergence   Many machine learning tasks are formulated as a nonconvex optimization
problem of minimizing the sum of a convex function and a composite function.
The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear
method, has been developed for such problems. The method iteratively solves
strongly convex subproblems with a damping term.
  This study proposes a new generalized LM method for solving the problem with
a smooth composite function. The method enjoys three theoretical guarantees:
iteration complexity bound, oracle complexity bound, and local convergence
under a H\"olderian growth condition. The local convergence results include
local quadratic convergence under the quadratic growth condition; this is the
first to extend a classical result for least-squares problems to a general
smooth composite function. In addition, this is the first LM method with both
an oracle complexity bound and local quadratic convergence under standard
assumptions. These results are achieved by carefully controlling the damping
parameter and solving the subproblems by the accelerated proximal gradient
method equipped with a particular termination condition. Experimental results
show that the proposed method performs well in practice for several instances,
including classification with a neural network and collaborative filtering with
nonnegative matrix factorization.

20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex