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On the equivalence of the method of conjugate gradients and quasi-Newton methods on quadratic problems

Anders Forsgren (andersf***at***kth.se)
Tove Odland (odland***at***kth.se)

Abstract: In this paper we state necessary and sufficient conditions for equivalence of the method of conjugate gradients and quasi-Newton methods on a quadratic problem. We show that the set of quasi-Newton schemes that generate parallel search directions to those of the method of conjugate gradients is strictly larger than the one-parameter Broyden family. In addition, we show that this set contains an infinite number of symmetric rank-one update schemes.

Keywords: method of conjugate gradients, quasi-Newton method, unconstrained quadratic program

Category 1: Nonlinear Optimization (Quadratic Programming )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: arXiv:1503.01892 [math.OC]

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Entry Submitted: 03/09/2015
Entry Accepted: 03/09/2015
Entry Last Modified: 03/09/2015

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