Online Semidefinite Programming
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.
online algorithms
semidefinite programming
primal-dual
40:1-40:13
Regular Paper
Noa
Elad
Noa Elad
Satyen
Kale
Satyen Kale
Joseph (Seffi)
Naor
Joseph (Seffi) Naor
10.4230/LIPIcs.ICALP.2016.40
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