We introduce a bundle method for the unconstrained minimization of non smooth difference-of-convex (DC) functions, and it is based on the calculation of a special type of descent direction called descent-ascent direction. The algorithm only requires evaluations of the minuend component function at each iterate, and it can be considered as a parsimonious bundle method as accumulation of information takes place only in case the descent-ascent direction does not provide a sufficient decrease. No line search is performed, and proximity control is pursued independent of whether the decrease in the objective function is achieved. Termination of the algorithm at a point satisfying a weak criticality condition is proved, and numerical results on a set of benchmark DC problems are reported.

The Descent–Ascent Algorithm for DC Programming

Pietro D’Alessandro;Manlio Gaudioso;Giovanni Giallombardo
;
Giovanna Miglionico
2024-01-01

Abstract

We introduce a bundle method for the unconstrained minimization of non smooth difference-of-convex (DC) functions, and it is based on the calculation of a special type of descent direction called descent-ascent direction. The algorithm only requires evaluations of the minuend component function at each iterate, and it can be considered as a parsimonious bundle method as accumulation of information takes place only in case the descent-ascent direction does not provide a sufficient decrease. No line search is performed, and proximity control is pursued independent of whether the decrease in the objective function is achieved. Termination of the algorithm at a point satisfying a weak criticality condition is proved, and numerical results on a set of benchmark DC problems are reported.
2024
nonsmooth optimization
difference of convex functions
bundle methods
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/362640
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