Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Grassmann condition number   We give new insight into the Grassmann condition of the conic feasibility
problem \[ x \in L \cap K \setminus\{0\}. \] Here $K\subseteq V$ is a regular
convex cone and $L\subseteq V$ is a linear subspace of the finite dimensional
Euclidean vector space $V$. The Grassmann condition of this problem is the
reciprocal of the distance from $L$ to the set of ill-posed instances in the
Grassmann manifold where $L$ lives.
  We consider a very general distance in the Grassmann manifold defined by two
possibly different norms in $V$. We establish the equivalence between the
Grassmann distance to ill-posedness of the above problem and a natural measure
of the least violated trial solution to its alternative feasibility problem. We
also show a tight relationship between the Grassmann and Renegar's condition
measures, and between the Grassman measure and a symmetry measure of the above
feasibility problem.
  Our approach can be readily specialized to a canonical norm in $V$ induced by
$K$, a prime example being the one-norm for the non-negative orthant. For this
special case we show that the Grassmann distance ill-posedness of is equivalent
to a measure of the most interior solution to the above conic feasibility
problem.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph