The Boosted DC Algorithm for Linearly Constrained DC Programming
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 proce...
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| Veröffentlicht in: | Set-valued and variational analysis Jg. 30; H. 4; S. 1265 - 1289 |
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01.12.2022
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| 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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| AbstractList | 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. |
| Author | Vuong, P. T. Campoy, R. Aragón-Artacho, F. J. |
| Author_xml | – sequence: 1 givenname: F. J. orcidid: 0000-0002-2445-8011 surname: Aragón-Artacho fullname: Aragón-Artacho, F. J. email: francisco.aragon@ua.es organization: Department of Mathematics, University of Alicante – sequence: 2 givenname: R. surname: Campoy fullname: Campoy, R. organization: Department of Statistics and Operational Research, Universitat de València – sequence: 3 givenname: P. T. surname: Vuong fullname: Vuong, P. T. organization: Mathematical Sciences School, University of Southampton |
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| CitedBy_id | crossref_primary_10_1016_j_ejor_2024_05_045 crossref_primary_10_1007_s10107_024_02190_0 crossref_primary_10_1007_s10107_024_02142_8 crossref_primary_10_1007_s11590_024_02167_0 |
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| Keywords | Boosted difference of convex functions algorithm 90C20 Global convergence Trust region subproblem 65K05 Copositivity problem Difference of convex functions 65K10 90C26 47N10 Constrained DC program |
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| SubjectTerms | Algorithms Analysis Constraints Convex analysis Mathematics Mathematics and Statistics Optimization |
| Title | The Boosted DC Algorithm for Linearly Constrained DC Programming |
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