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Incremental bundle methods using upper models

van Ackooij, Wim and Frangioni, Antonio (2016) Incremental bundle methods using upper models. Technical Report del Dipartimento di Informatica, TR . University of Pisa, Pisa, IT. (Submitted)

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    We propose a family of proximal bundle methods for minimizing sum-structured convex nondifferentiable functions which require two slightly uncommon assumptions, that are satisfied in many relevant applications: Lipschitz continuity of the functions and oracles which also produce upper estimates on the function values. In exchange, the methods: i) use upper models of the functions that allow to estimate function values at points where the oracle has not been called; ii) provide the oracles with more information about when the function computation can be interrupted, possibly diminishing their cost; iii) allow to skip oracle calls entirely for some of the component functions, not only at ``null steps'' but also at ``serious steps''; iv) provide explicit and reliable a-posteriori estimates of the quality of the obtained solutions; v) work with all possible combinations of different assumptions on the oracles. We also discuss introduction of constraints (or, more generally, of easy components) and use of (partly) aggregated models.

    Item Type: Book
    Uncontrolled Keywords: Nonsmooth optimization, bundle methods, incremental approach
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/09 - Ricerca operativa
    Divisions: Dipartimenti (from 2013) > DIPARTIMENTO DI INFORMATICA
    Depositing User: Prof. Antonio Frangioni
    Date Deposited: 02 Sep 2016 13:06
    Last Modified: 02 Sep 2016 13:06
    URI: http://eprints.adm.unipi.it/id/eprint/2357

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