Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong duality of a conic optimization problem with a single hyperplane
  and two cone constraints   Our target conic optimization problem (COP) is minimizing a linear function
in a vector variable $x$ subject to a single hyperplane constraint $x \in H$
and two cone constraints $x \in K_1$, $x \in K_2$. This COP is geometrically
representable and extensive enough to study strong (Lagrangian) duality of more
general COPs with cone and multiple linear inequality constraints. It can also
be identically reformulated as a simpler COP with the single hyperplane
constraint $x \in H$ and the single cone constraint $x \in K_1 \cap K_2$, which
has no duality gap without any constraint qualification. The dual of the
original target COP is equivalent to the dual of the reformulated COP if the
Minkowski sum of the duals of the two cones $K_1$ and $K_2$ is closed or if the
dual of the reformulated COP satisfies a Slater condition. Thus, these two
conditions make it possible to transfer all duality results, including the
existence and/or boundedness of optimal solutions, on the reformulated COP to
the ones on the original target COP, and further to the ones on a standard
primal-dual pair of COPs with symmetry.

6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin