Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Efficient Inexact ABCD Method for Least Squares Semidefinite
  Programming   We consider least squares semidefinite programming (LSSDP) where the primal
matrix variable must satisfy given linear equality and inequality constraints,
and must also lie in the intersection of the cone of symmetric positive
semidefinite matrices and a simple polyhedral set. We propose an inexact
accelerated block coordinate descent (ABCD) method for solving LSSDP via its
dual, which can be reformulated as a convex composite minimization problem
whose objective is the sum of a coupled quadratic function involving four
blocks of variables and two separable non-smooth functions involving only the
first and second block, respectively. Our inexact ABCD method has the
attractive $O(1/k^2)$ iteration complexity if the subproblems are solved
progressively more accurately. The design of our ABCD method relies on recent
advances in the symmetric Gauss-Seidel technique for solving a convex
minimization problem whose objective is the sum of a multi-block quadratic
function and a non-smooth function involving only the first block. Extensive
numerical experiments on various classes of over 600 large scale LSSDP problems
demonstrate that our proposed ABCD method not only can solve the problems to
high accuracy, but it is also far more efficient than (a) the well known BCD
(block coordinate descent) method, (b) the eARBCG (an enhanced version of the
accelerated randomized block coordinate gradient) method, and (c) the APG
(accelerated proximal gradient) method.

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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom