- Title
- Bundle enrichment method for nonsmooth difference of convex programming problems
- Creator
- Gaudioso, Manilo; Taheri, Sona; Bagirov, Adil; Karmitsa, Napsu
- Date
- 2023
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/197189
- Identifier
- vital:18816
- Identifier
-
https://doi.org/10.3390/a16080394
- Identifier
- ISSN:1999-4893 (ISSN)
- Abstract
- 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. © 2023 by the authors.
- Publisher
- Multidisciplinary Digital Publishing Institute (MDPI)
- Relation
- Algorithms Vol. 16, no. 8 (2023), p.; http://purl.org/au-research/grants/arc/DP190100580
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- https:// creativecommons.org/licenses/by/ 4.0/
- Rights
- Copyright ©2023 by the authors
- Rights
- Open Access
- Subject
- 40 Engineering; 46 Information and computing sciences; 49 Mathematical sciences; Bundle method; Cutting plane; DC optimization; Nonconvex nonsmooth optimization
- Full Text
- Reviewed
- Funder
- A.M. Bagirov’s research is funded by the Australian Government through the Australian Research Council’s Discovery Projects (Project No. DP190100580), and the research by N. Karmitsa is supported by the Academy of Finland (Projects No. 345804 and No. 345805). Funding text 2: A.M. Bagirov’s research is funded by the Australian Government through the Australian Research Council’s Discovery Projects (Project No. DP190100580), and the research by N. Karmitsa is supported by the Research Council of Finland (Projects No. 345804 and No. 345805).
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