Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Semismooth Newton-Type Method for the Nearest Doubly Stochastic Matrix
  Problem   We study a semismooth Newton-type method for the nearest doubly stochastic
matrix problem where both differentiability and nonsingularity of the Jacobian
can fail. The optimality conditions for this problem are formulated as a system
of strongly semismooth functions. We show that the so-called local error bound
condition does not hold for this system. Thus the guaranteed convergence rate
of Newton-type methods is at most superlinear. By exploiting the problem
structure, we construct a modified two step semismooth Newton method that
guarantees a nonsingular Jacobian matrix at each iteration, and that converges
to the nearest doubly stochastic matrix quadratically. To the best of our
knowledge, this is the first Newton-type method which converges
$Q$-quadratically in the absence of the local error bound condition.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci