Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interior-point methods for second-order stationary points of nonlinear
  semidefinite optimization problems using negative curvature   We propose a primal-dual interior-point method (IPM) with convergence to
second-order stationary points (SOSPs) of nonlinear semidefinite optimization
problems, abbreviated as NSDPs. As far as we know, the current algorithms for
NSDPs only ensure convergence to first-order stationary points such as
Karush-Kuhn-Tucker points. The proposed method generates a sequence
approximating SOSPs while minimizing a primal-dual merit function for NSDPs by
using scaled gradient directions and directions of negative curvature. Under
some assumptions, the generated sequence accumulates at an SOSP with a
worst-case iteration complexity. This result is also obtained for a primal IPM
with slight modification. Finally, our numerical experiments show the benefits
of using directions of negative curvature in the proposed method.

22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin