New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts
In this paper, we consider the nonconvex extended trust-region subproblem with two intersecting linear inequality constraints, $(\mathrm{ETR}_2)$, and use a sequence of semi-definite programming (SDP) problems with second-order-cone(SOC) constraints to eliminate the duality gap of the SOC reformulat...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.661/ |
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| author | Wang, Meiling |
| author_facet | Wang, Meiling |
| author_sort | Wang, Meiling |
| collection | DOAJ |
| description | In this paper, we consider the nonconvex extended trust-region subproblem with two intersecting linear inequality constraints, $(\mathrm{ETR}_2)$, and use a sequence of semi-definite programming (SDP) problems with second-order-cone(SOC) constraints to eliminate the duality gap of the SOC reformulation for $(\mathrm{ETR}_2)$. We first narrow the duality gap of the SOC reformulation by adding a new appropriate SOC constraint, and a sufficient condition is presented to characterize when the new SOC constraint is valid. Then we establish an iterative algorithm and the results of numerical experiments show that the iterative algorithm works efficiently in eliminating the SDPR-SOCR gap of $(\mathrm{ETR}_2)$. |
| format | Article |
| id | doaj-art-ed07a074488a42518c4779404595361a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-ed07a074488a42518c4779404595361a2025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111497151310.5802/crmath.66110.5802/crmath.661New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cutsWang, Meiling0School of Statistics and Data Science, Beijing Wuzi University, Beijing 101149, ChinaIn this paper, we consider the nonconvex extended trust-region subproblem with two intersecting linear inequality constraints, $(\mathrm{ETR}_2)$, and use a sequence of semi-definite programming (SDP) problems with second-order-cone(SOC) constraints to eliminate the duality gap of the SOC reformulation for $(\mathrm{ETR}_2)$. We first narrow the duality gap of the SOC reformulation by adding a new appropriate SOC constraint, and a sufficient condition is presented to characterize when the new SOC constraint is valid. Then we establish an iterative algorithm and the results of numerical experiments show that the iterative algorithm works efficiently in eliminating the SDPR-SOCR gap of $(\mathrm{ETR}_2)$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.661/Second-order-cone reformulationextended trust-region subproblemlinear inequality constraintsduality gapsemidefinite programming relaxation |
| spellingShingle | Wang, Meiling New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts Comptes Rendus. Mathématique Second-order-cone reformulation extended trust-region subproblem linear inequality constraints duality gap semidefinite programming relaxation |
| title | New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts |
| title_full | New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts |
| title_fullStr | New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts |
| title_full_unstemmed | New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts |
| title_short | New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts |
| title_sort | new results on eliminating the duality gap of the second order cone reformulation for extended trust region subproblem with two intersecting cuts |
| topic | Second-order-cone reformulation extended trust-region subproblem linear inequality constraints duality gap semidefinite programming relaxation |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.661/ |
| work_keys_str_mv | AT wangmeiling newresultsoneliminatingthedualitygapofthesecondorderconereformulationforextendedtrustregionsubproblemwithtwointersectingcuts |