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A Nonmonotone Proximal Bundle Method With (Potentially) Continuous Step Decisions

Astorino, Annabella and Frangioni, Antonio and Fuduli, Antonio and Gorgone, Enrico (2012) A Nonmonotone Proximal Bundle Method With (Potentially) Continuous Step Decisions. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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    We discuss a numerical algorithm for minimization of a convex nondifferentiable function belonging to the family of proximal bundle methods. Unlike all of its brethren, the approach does not rely on measuring descent of the objective function at the so-called ``serious steps'', while ``null steps'' only serve at improving the descent direction in case of unsuccessful steps. Rather, a merit function is defined which is decreased at each iteration, leading to a (potentially) continuous choice of the stepsize between zero (the null step) and one (the serious step). By avoiding the discrete choice the convergence analysis is simplified, and we can more easily obtain efficiency estimates for the method. Simple choices for the step selection actually reproduce the dichotomic 0/1 behavior of standard proximal bundle methods, but shedding new light on the rationale behind the process, and ultimately with different rules. Yet, using nonlinear upper models of the function in the step selection process can lead to actual fractional steps.

    Item Type: Book
    Uncontrolled Keywords: Nonsmooth optimization, bundle methods, nonmonotone algorithm
    Subjects: Area01 - Scienze matematiche e informatiche > INF/01 - Informatica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: dott.ssa Sandra Faita
    Date Deposited: 03 Dec 2014 18:24
    Last Modified: 03 Dec 2014 18:24
    URI: http://eprints.adm.unipi.it/id/eprint/2292

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