License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.40
URN: urn:nbn:de:0030-drops-63205
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6320/
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Elad, Noa ; Kale, Satyen ; Naor, Joseph (Seffi)

Online Semidefinite Programming

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LIPIcs-ICALP-2016-40.pdf (0.4 MB)

Abstract

We consider semidefinite programming through the lens of online algorithms - what happens if not all input is given at once, but rather iteratively? In what way does it make sense for a semidefinite program to be revealed? We answer these questions by defining a model for online semidefinite programming. This model can be viewed as a generalization of online coveringpacking linear programs, and it also captures interesting problems from quantum information theory. We design an online algorithm for semidefinite programming, utilizing the online primaldual method, achieving a competitive ratio of O(log(n)), where n is the number of matrices in the primal semidefinite program. We also design an algorithm for semidefinite programming with box constraints, achieving a competitive ratio of O(log F*), where F* is a sparsity measure of the semidefinite program. We conclude with an online randomized rounding procedure.

BibTeX - Entry

@InProceedings{elad_et_al:LIPIcs:2016:6320,
  author =	{Noa Elad and Satyen Kale and Joseph (Seffi) Naor},
  title =	{{Online Semidefinite Programming}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{40:1--40:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6320},
  URN =		{urn:nbn:de:0030-drops-63205},
  doi =		{10.4230/LIPIcs.ICALP.2016.40},
  annote =	{Keywords: online algorithms, semidefinite programming, primal-dual}
}

Keywords: online algorithms, semidefinite programming, primal-dual
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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