The Descent–Ascent Algorithm for DC Programming

Pietro D’Alessandro (), Manlio Gaudioso (), Giovanni Giallombardo () and Giovanna Miglionico ()
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Pietro D’Alessandro: Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy
Manlio Gaudioso: Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy
Giovanni Giallombardo: Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy
Giovanna Miglionico: Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy

INFORMS Journal on Computing, 2024, vol. 36, issue 2, 657-671

Abstract: We introduce a bundle method for the unconstrained minimization of nonsmooth 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.

Keywords: nonsmooth optimization; difference of convex functions; bundle methods (search for similar items in EconPapers)
Date: 2024
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