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Generalized Bundle Methods

Frangioni, Antonio (1998) Generalized Bundle Methods. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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    We propose a class of generalized Bundle methods where the stabilizi= term can be any closed convex function satisfying certain properties. = We prove finite termination, asymptotic convergence and finite convergenc= e to an optimal point of different variants of the algorithm: for some of= these proofs, f-regularity of the function (a new generalization of inf-= compactness) is required. Our analysis gives a unified convergence proof = for several classes of Bundle methods that have been so far regarded as d= istinct, enhancing on the results known for some of them: furthermore, it= covers methods proposed in the literature that had not previously been r= ecognised as Bundle methods. A novelty in our approach is the proposal of= a dual for the minimization problem: we show that Bundle methods can be = seen as a dual ascent approach to one single nonlinear problem in the dua= l space, where nonlinear subproblems are approximately solved at each ste= p with an inner linearization approach. This interpretation is particular= ly

    Item Type: Book
    Uncontrolled Keywords: NonDifferentiable Optimization, Bundle methods, Lagrangean Duals
    Subjects: Area01 - Scienze matematiche e informatiche > INF/01 - Informatica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: dott.ssa Sandra Faita
    Date Deposited: 26 Jan 2015 14:31
    Last Modified: 26 Jan 2015 14:31
    URI: http://eprints.adm.unipi.it/id/eprint/1993

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