Polynomial Linear Programming with Gaussian Belief Propagation

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dc.creatorBickson, Danny
dc.creatorTock, Yoav
dc.creatorShental, Ori
dc.creatorDolev, Danny
dc.date2008-10-09
dc.date.accessioned2026-07-07T13:04:05Z
dc.date.available2026-07-07T13:04:05Z
dc.descriptionInterior-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(n^{3.5}), 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-point algorithm which uses the Newton method, including non-linear program solvers.
dc.description7 pages, 1 figure, appeared in the 46th Annual Allerton Conference on Communication, Control and Computing, Allerton House, Illinois, Sept. 2008
dc.identifierhttps://arxiv.org/abs/0810.1631
dc.identifierhttp://arxiv.org/abs/0810.1631
dc.identifierThe 46th Annual Allerton Conference on Communication, Control and Computing, Allerton House, Illinois, Sept. 2008
dc.identifierdoi:10.1109/ALLERTON.2008.4797652
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227032
dc.subjectInformation Theory
dc.subjectE.5
dc.titlePolynomial Linear Programming with Gaussian Belief Propagation
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