The continuous quadrant penalty formulation of logical constraints

Sonia Cafieri (1) , Andrew R. Conn , Marcel Mongeau (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

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.

Mots clés: Logical constraints; penalty function; continuous optimization; aircraft conflicts

Domaines: Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]

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⟩