L-Broyden methods: a generalization of the L-BFGS method to the limited-memory Broyden family
Reed, M. B., 2009. L-Broyden methods: a generalization of the L-BFGS method to the limited-memory Broyden family. International Journal of Computer Mathematics, 86 (4), pp. 606-615.
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The paper derives a multiplicative update equation for the convex Broyden family of quasi-Newton (QN) updates. The well-known multiplicative Broyden-fletcher-Goldfarb-Shanno (BFGS) update is a special case of this. Using a self-scaling parameter, the formula is extended to the SR1 update. It is shown that for each Broyden update, a pair of multiplicative update formulae can be defined (coincident in the case of Davidon-fletcher-Powell (DFP)). The multiplicative updates are used to define limited-memory QN algorithms, denoted the L-Broyden methods, of which L-BFGS is a special case. Numerical results show that the L-Broyden methods are competitive with extensions of the variable storage conjugate gradients limited memory QN method to other Broyden updates, but that L-BFGS with Shanno scaling remains the most efficient and reliable method in the L-Broyden family.
|Creators||Reed, M. B.|
|Uncontrolled Keywords||limited memory, quasi-newton methods, unconstrained optimisation|
|Departments||Faculty of Science > Mathematical Sciences|
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