Open Journal of Mathematical Optimization

The continuous quadrant penalty formulation of logical constraints
Sonia Cafieri1; Andrew R. Conn2; Marcel Mongeau1
1 ENAC, Université de Toulouse, France
2 IBM T.J. Watson Research Center, NY, USA
Open Journal of Mathematical Optimization, Volume 4 (2023), article no. 7, 12 p.

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.

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Accepted:
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DOI: 10.5802/ojmo.28
Keywords: Logical constraints, penalty function, continuous optimization, aircraft conflicts
Sonia Cafieri 1; Andrew R. Conn 2; Marcel Mongeau 1

1 ENAC, Université de Toulouse, France
2 IBM T.J. Watson Research Center, NY, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Sonia Cafieri; Andrew R. Conn; Marcel Mongeau. The continuous quadrant penalty formulation of logical constraints. Open Journal of Mathematical Optimization, Volume 4 (2023), article  no. 7, 12 p. doi : 10.5802/ojmo.28. https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.28/

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