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A strong polynomial gradient algorithm in Linear Programming

P A Bruijs (p.a.bruijs***at***wxs.nl)

Abstract: It has been an open question whether the Linear Programming (LP) problem can be solved in strong polynomial time. The simplex algorithm does not offer a polynomial bound, and polynomial algorithms by Khachiyan and Karmarkar donít have the strong characteristic. The curious fact that non-linear algorithms would be needed to deliver the strongest complexity result for LP served as the motivation to look at feasible gradient methods. Experiments and theory show that a linear algorithm has the desired strong characteristic.

Keywords: linear programming - simplex algorithm - ellipsoid method - interior-point methods - gradient methods - computational complexity

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: unpublished, no affiliation

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Entry Submitted: 03/23/2015
Entry Accepted: 03/23/2015
Entry Last Modified: 03/31/2015

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