Abstract
The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation step from the point computed by DCA via a line search procedure. In this work, we propose an extension of BDCA that can be applied to difference of convex functions programs with linear constraints, and prove that every cluster point of the sequence generated by this algorithm is a Karush–Kuhn–Tucker point of the problem if the feasible set has a Slater point. When the objective function is quadratic, we prove that any sequence generated by the algorithm is bounded and R-linearly (geometrically) convergent. Finally, we present some numerical experiments where we compare the performance of DCA and BDCA on some challenging problems: to test the copositivity of a given matrix, to solve one-norm and infinity-norm trust-region subproblems, and to solve piecewise quadratic problems with box constraints. Our numerical results demonstrate that this new extension of BDCA outperforms DCA.
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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
The authors would like to thank the referees for their careful reading and their constructive comments which helped to improve our manuscript.
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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. FJAA and RC were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission (PGC2018-097960-B-C22), and by the Generalitat Valenciana (AICO/2021/165). PTV was supported by Vietnam Ministry of Education and Training Project hosting by the University of Technology and Education, Ho Chi Minh City Vietnam (2023-2024).
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Dedicated to Professor Miguel A. Goberna on the occasion of his 70th birthday
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Aragón-Artacho, F.J., Campoy, R. & Vuong, P.T. The Boosted DC Algorithm for Linearly Constrained DC Programming. Set-Valued Var. Anal 30, 1265–1289 (2022). https://doi.org/10.1007/s11228-022-00656-x
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DOI: https://doi.org/10.1007/s11228-022-00656-x
Keywords
- Difference of convex functions
- Boosted difference of convex functions algorithm
- Global convergence
- Constrained DC program
- Copositivity problem
- Trust region subproblem