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• W3135112727 abstract "In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However, in contrast to the classical quasi-Newton methods, which use the difference of successive iterates for updating the Hessian approximations, our methods apply basis vectors, greedily selected so as to maximize a certain measure of progress. For greedy quasi-Newton methods, we establish an explicit non-asymptotic bound on their rate of local superlinear convergence, which contains a contraction factor, depending on the square of the iteration counter. We also show that these methods produce Hessian approximations whose deviation from the exact Hessians linearly convergences to zero." @default.
• W3135112727 created "2021-03-15" @default.
• W3135112727 creator A5062011745 @default.
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• W3135112727 date "2021-01-01" @default.
• W3135112727 modified "2023-09-26" @default.
• W3135112727 title "Greedy Quasi-Newton Methods with Explicit Superlinear Convergence" @default.
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• W3135112727 doi "https://doi.org/10.1137/20m1320651" @default.
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