eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-23
40:1
40:13
10.4230/LIPIcs.ICALP.2016.40
article
Online Semidefinite Programming
Elad, Noa
Kale, Satyen
Naor, Joseph (Seffi)
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol055-icalp2016/LIPIcs.ICALP.2016.40/LIPIcs.ICALP.2016.40.pdf
online algorithms
semidefinite programming
primal-dual