Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A weak constraint qualification for conic programs and a problem on
  duality gap   We discuss a weak constraint qualification for conic linear programs and its
applications for a few classes of cones. This constraint qualification is used
to give a solution to a problem proposed by Shapiro and Z\v{a}linescu and show
that if a closed convex cone is such that all its non-trivial faces are
polyhedral and all the non-trivial exposed faces of its dual are polyhedral,
then the duality gap is zero as long as the primal and dual problems are
feasible. Moreover, the common optimal value must be attained at least at one
of the sides. We also show an example of a cone that meets the requirements our
theorem but is such that previously known results cannot be used to prove its
good duality properties.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th