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arXiv · 1201.5135

Faster and Simpler Width-Independent Parallel Algorithms for Positive Semidefinite Programming

Richard Peng·Kanat Tangwongsan·Peng Zhang
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Abstract

This paper studies the problem of finding an $(1+\epsilon)$-approximate solution to positive semidefinite programs. These are semidefinite programs in which all matrices in the constraints and objective are positive semidefinite and all scalars are non-negative. We present a simpler \NC parallel algorithm that on input with $n$ constraint matrices, requires $O(\frac{1}{\epsilon^3} log^3 n)$ iterations, each of which involves only simple matrix operations and computing the trace of the product of a matrix exponential and a positive semidefinite matrix. Further, given a positive SDP in a factorized form, the total work of our algorithm is nearly-linear in the number of non-zero entries in the factorization.

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Richard Peng, Kanat Tangwongsan, Peng Zhang. 2012-01-24. Faster and Simpler Width-Independent Parallel Algorithms for Positive Semidefinite Programming. https://arxiv.org/abs/1201.5135

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