Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimal-Storage Approach to Semidefinite Programming using
  Approximate Complementarity   This paper develops a new storage-optimal algorithm that provably solves
generic semidefinite programs (SDPs) in standard form. This method is
particularly effective for weakly constrained SDPs. The key idea is to
formulate an approximate complementarity principle: Given an approximate
solution to the dual SDP, the primal SDP has an approximate solution whose
range is contained in the eigenspace with small eigenvalues of the dual slack
matrix. For weakly constrained SDPs, this eigenspace has very low dimension, so
this observation significantly reduces the search space for the primal
solution.
  This result suggests an algorithmic strategy that can be implemented with
minimal storage:
  (1) Solve the dual SDP approximately;
  (2) compress the primal SDP to the eigenspace with small eigenvalues of the
dual slack matrix;
  (3) solve the compressed primal SDP.
  The paper also provides numerical experiments showing that this approach is
successful for a range of interesting large-scale SDPs.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ