Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Limiting Analysis on Regularization of Singular SDP and its
  Implication to Infeasible Interior-point Algorithms   We consider primal-dual pairs of semidefinite programs and assume that they
are ill-posed, i.e., both primal and dual are either weakly feasible or weakly
infeasible. Under such circumstances, strong duality may break down and the
primal and dual might have a nonzero duality gap. Nevertheless, there are
arbitrary small perturbations to the problem data which makes the perturbed
primal-dual pair strongly feasible thus zeroing the duality gap. In this paper,
we conduct an asymptotic analysis of the optimal value as the perturbation is
driven to zero. Specifically, we fix two positive definite matrices (typically
the identity matrices), and shift the associated affine spaces of the primal
and dual slightly in the direction of the two positive definite matrices
possibly in a different proportion so that the perturbed problems have interior
feasible solutions, and analyze the behavior of the optimal value of the
perturbed problem when the perturbation is reduced to zero keeping the
proportion. A key feature of our analysis is that no further assumptions such
as compactness or constraint qualifications are ever made. It will be shown
that the optimal value of the perturbed problem converges to a value between
the primal and dual optimal values of the original problem. Finally, the
analysis leads us to the relatively surprising consequence that the infeasible
interior-point algorithms for SDP generates a sequence converging to a number
between the primal and dual optimal values, even in the presence of a nonzero
duality gap. We expect that this property might be particularly useful in
solving mixed integer SDPs with infeasible interior-point methods.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph