Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Efficient Inexact Newton-CG Algorithm for the Smallest Enclosing Ball
  Problem of Large Dimensions   In this paper, we consider the problem of computing the smallest enclosing
ball (SEB) of a set of $m$ balls in $\mathbb{R}^n,$ where the product $mn$ is
large. We first approximate the non-differentiable SEB problem by its
log-exponential aggregation function and then propose a computationally
efficient inexact Newton-CG algorithm for the smoothing approximation problem
by exploiting its special (approximate) sparsity structure. The key difference
between the proposed inexact Newton-CG algorithm and the classical Newton-CG
algorithm is that the gradient and the Hessian-vector product are inexactly
computed in the proposed algorithm, which makes it capable of solving the
large-scale SEB problem. We give an adaptive criterion of inexactly computing
the gradient/Hessian and establish global convergence of the proposed
algorithm. We illustrate the efficiency of the proposed algorithm by using the
classical Newton-CG algorithm as well as the algorithm from [Zhou. {et al.} in
Comput. Opt. \& Appl. 30, 147--160 (2005)] as benchmarks.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th