{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T13:28:57Z","timestamp":1769088537447,"version":"3.49.0"},"reference-count":48,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T00:00:00Z","timestamp":1692576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Australian Government through the Australian Research Council\u2019s Discovery Projects","award":["DP190100580"],"award-info":[{"award-number":["DP190100580"]}]},{"name":"Australian Government through the Australian Research Council\u2019s Discovery Projects","award":["345804"],"award-info":[{"award-number":["345804"]}]},{"name":"Australian Government through the Australian Research Council\u2019s Discovery Projects","award":["345805"],"award-info":[{"award-number":["345805"]}]},{"name":"Research Council of Finland","award":["DP190100580"],"award-info":[{"award-number":["DP190100580"]}]},{"name":"Research Council of Finland","award":["345804"],"award-info":[{"award-number":["345804"]}]},{"name":"Research Council of Finland","award":["345805"],"award-info":[{"award-number":["345805"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a16080394","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:46:22Z","timestamp":1692665182000},"page":"394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Bundle Enrichment Method for Nonsmooth Difference of Convex Programming Problems"],"prefix":"10.3390","volume":"16","author":[{"given":"Manlio","family":"Gaudioso","sequence":"first","affiliation":[{"name":"DIMES (Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica), Universit\u00e0 della Calabria, 87036 Rende, CS, Italy"}]},{"given":"Sona","family":"Taheri","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, RMIT University, Melbourne 3000, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2075-1699","authenticated-orcid":false,"given":"Adil M.","family":"Bagirov","sequence":"additional","affiliation":[{"name":"Centre for Smart Analytics, Institute of Innovation, Science and Sustainability, Federation University Australia, Ballarat 3350, Australia"}]},{"given":"Napsu","family":"Karmitsa","sequence":"additional","affiliation":[{"name":"Department of Computing, University of Turku, FI-20014 Turku, Finland"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,21]]},"reference":[{"key":"ref_1","unstructured":"Bertsekas, D.P. 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