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Greedy quasi-Newton methods with explicit superlinear convergence

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  • RODOMANOV Anton,

    (Université catholique de Louvain, CORE, Belgium)

  • NESTEROV Yurii,

    (Université catholique de Louvain, CORE, Belgium)

Abstract

In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating forulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS ans 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 estabish an explicit non-asymptotic bound on their rate of local superlinear convergence, which contains a contracting 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.

Suggested Citation

  • RODOMANOV Anton, & NESTEROV Yurii,, 2020. "Greedy quasi-Newton methods with explicit superlinear convergence," LIDAM Discussion Papers CORE 2020006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2020006
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    More about this item

    Keywords

    quasi-Newton methods; Broyden family; SR1; DFP; BFGS; superlinear convergence; local convergence; rate of convergence;
    All these keywords.

    JEL classification:

    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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