Refereed journal article or data article (A1)
Bundle Enrichment Method for Nonsmooth Difference of Convex Programming Problems
List of Authors: Gaudioso Manlio, Taheri Sona, Bagirov Adil M., Karmitsa Napsu
Publisher: MDPI
Publication year: 2023
Journal: Algorithms
Journal name in source: ALGORITHMS
Journal acronym: ALGORITHMS
Article number: 394
Volume number: 16
Issue number: 8
Number of pages: 21
eISSN: 1999-4893
DOI: http://dx.doi.org/10.3390/a16080394
URL: https://www.mdpi.com/1999-4893/16/8/394
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/181176791
The Bundle Enrichment Method (BEM-DC) is introduced for solving nonsmooth difference of convex (DC) programming problems. The novelty of the method consists of the dynamic management of the bundle. More specifically, a DC model, being the difference of two convex piecewise affine functions, is formulated. The (global) minimization of the model is tackled by solving a set of convex problems whose cardinality depends on the number of linearizations adopted to approximate the second DC component function. The new bundle management policy distributes the information coming from previous iterations to separately model the DC components of the objective function. Such a distribution is driven by the sign of linearization errors. If the displacement suggested by the model minimization provides no sufficient decrease of the objective function, then the temporary enrichment of the cutting plane approximation of just the first DC component function takes place until either the termination of the algorithm is certified or a sufficient decrease is achieved. The convergence of the BEM-DC method is studied, and computational results on a set of academic test problems with nonsmooth DC objective functions are provided.
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