Chen Chen, Yoav Tock, et al.
DEBS 2018
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-point algorithm which uses the Newton method, including non-linear program solvers. © 2008 IEEE.
Chen Chen, Yoav Tock, et al.
DEBS 2018
Danny Bickson, Tzachy Reinman, et al.
Peer-to-Peer Networking and Applications
A. Manzalini, R. Minerva, et al.
ICIN 2013
Artem Barger, Liran Funaro, et al.
ICBC 2023