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Article Dans Une Revue Open Journal of Mathematical Optimization Année : 2023

The continuous quadrant penalty formulation of logical constraints

Sonia Cafieri
Andrew R. Conn
  • Fonction : Auteur
Marcel Mongeau

Résumé

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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Dates et versions

hal-03623407 , version 1 (27-04-2022)
hal-03623407 , version 2 (23-01-2024)

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Sonia Cafieri, Andrew R. Conn, Marcel Mongeau. The continuous quadrant penalty formulation of logical constraints. Open Journal of Mathematical Optimization, 2023, pp.1-12. ⟨10.5802/ojmo.28⟩. ⟨hal-03623407v2⟩
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