The continuous quadrant penalty formulation of logical constraints
Could continuous optimization address efficiently logical constraints? We propose a continuous-optimization alternative to the usual discrete-optimization (big-M and complementary) formulations of logical constraints, that can lead to effective practical methods. Based on the simple idea of guiding...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2023-09-01
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| Series: | Open Journal of Mathematical Optimization |
| Subjects: | |
| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.28/ |
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| _version_ | 1825204992730988544 |
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| author | Cafieri, Sonia Conn, Andrew R. Mongeau, Marcel |
| author_facet | Cafieri, Sonia Conn, Andrew R. Mongeau, Marcel |
| author_sort | Cafieri, Sonia |
| collection | DOAJ |
| description | Could continuous optimization address efficiently logical constraints? We propose a continuous-optimization alternative to the usual discrete-optimization (big-M and complementary) formulations of logical constraints, that can lead to effective practical methods. Based on the simple idea of guiding the search of a continuous-optimization descent method towards the parts of the domain where the logical constraint is satisfied, we introduce a smooth penalty-function formulation of logical constraints, and related theoretical results. This formulation allows a direct use of state-of-the-art continuous optimization solvers. The effectiveness of the continuous quadrant penalty formulation is demonstrated on an aircraft conflict avoidance application. |
| format | Article |
| id | doaj-art-8675306bca67479ba0de6c41e7f568b8 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-8675306bca67479ba0de6c41e7f568b82025-02-07T14:02:56ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602023-09-01411210.5802/ojmo.2810.5802/ojmo.28The continuous quadrant penalty formulation of logical constraintsCafieri, Sonia0Conn, Andrew R.1Mongeau, Marcel2ENAC, Université de Toulouse, FranceIBM T.J. Watson Research Center, NY, USAENAC, Université de Toulouse, FranceCould continuous optimization address efficiently logical constraints? We propose a continuous-optimization alternative to the usual discrete-optimization (big-M and complementary) formulations of logical constraints, that can lead to effective practical methods. Based on the simple idea of guiding the search of a continuous-optimization descent method towards the parts of the domain where the logical constraint is satisfied, we introduce a smooth penalty-function formulation of logical constraints, and related theoretical results. This formulation allows a direct use of state-of-the-art continuous optimization solvers. The effectiveness of the continuous quadrant penalty formulation is demonstrated on an aircraft conflict avoidance application.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.28/Logical constraintspenalty functioncontinuous optimizationaircraft conflicts |
| spellingShingle | Cafieri, Sonia Conn, Andrew R. Mongeau, Marcel The continuous quadrant penalty formulation of logical constraints Open Journal of Mathematical Optimization Logical constraints penalty function continuous optimization aircraft conflicts |
| title | The continuous quadrant penalty formulation of logical constraints |
| title_full | The continuous quadrant penalty formulation of logical constraints |
| title_fullStr | The continuous quadrant penalty formulation of logical constraints |
| title_full_unstemmed | The continuous quadrant penalty formulation of logical constraints |
| title_short | The continuous quadrant penalty formulation of logical constraints |
| title_sort | continuous quadrant penalty formulation of logical constraints |
| topic | Logical constraints penalty function continuous optimization aircraft conflicts |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.28/ |
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