Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Hessian-Free Methods for Checking the Second-Order Sufficient Conditions
  in Equality-Constrained Optimization and Equilibrium Problems
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
3
The categories of this paper are: physics