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CORR
2008
Springer

Polynomial Linear Programming with Gaussian Belief Propagation

8 years 2 months ago
Polynomial Linear Programming with Gaussian Belief Propagation
Abstract--Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n3.5 ), where n is the number of unknown variables. Karmarkar's celebrated algorithm is known to be an instance of the log-barrier method using the Newton iteration. The main computational overhead of this method is in inverting the Hessian matrix of the Newton iteration. In this contribution, we propose the application of the Gaussian belief propagation (GaBP) algorithm as part of an efficient and distributed LP solver that exploits the sparse and symmetric structure of the Hessian matrix and avoids the need for direct matrix inversion. This approach shifts the computation from realm of linear algebra to that of probabilistic inference on graphical models, thus applying GaBP as an efficient inference engine. Our construction is general and can be used for any interior-...
Danny Bickson, Yoav Tock, Ori Shental, Danny Dolev
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Danny Bickson, Yoav Tock, Ori Shental, Danny Dolev
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