Geodesic
The continuous quadrant penalty formulation of logical constraints
Cafieri, Sonia1 ; Conn, Andrew R.2 ; Mongeau, Marcel1
1 ENAC, Université de Toulouse, France
2 IBM T.J. Watson Research Center, NY, USA
Open Journal of Mathematical Optimization, Tome 4 (2023), article no. 7, 12 p.

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/ojmo.28
Keywords: Logical constraints, penalty function, continuous optimization, aircraft conflicts

Cafieri, Sonia 1 ; Conn, Andrew R. 2 ; Mongeau, Marcel 1

1 ENAC, Université de Toulouse, France
2 IBM T.J. Watson Research Center, NY, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{OJMO_2023__4__A7_0,
     author = {Cafieri, Sonia and Conn, Andrew R. and Mongeau, Marcel},
     title = {The continuous quadrant penalty formulation of logical constraints},
     journal = {Open Journal of Mathematical Optimization},
     eid = {7},
     pages = {1--12},
     publisher = {Universit\'e de Montpellier},
     volume = {4},
     year = {2023},
     doi = {10.5802/ojmo.28},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/ojmo.28/}
}
TY  - JOUR
AU  - Cafieri, Sonia
AU  - Conn, Andrew R.
AU  - Mongeau, Marcel
TI  - The continuous quadrant penalty formulation of logical constraints
JO  - Open Journal of Mathematical Optimization
PY  - 2023
SP  - 1
EP  - 12
VL  - 4
PB  - Université de Montpellier
UR  - http://geodesic.mathdoc.fr/articles/10.5802/ojmo.28/
DO  - 10.5802/ojmo.28
LA  - en
ID  - OJMO_2023__4__A7_0
ER  - 
%0 Journal Article
%A Cafieri, Sonia
%A Conn, Andrew R.
%A Mongeau, Marcel
%T The continuous quadrant penalty formulation of logical constraints
%J Open Journal of Mathematical Optimization
%D 2023
%P 1-12
%V 4
%I Université de Montpellier
%U http://geodesic.mathdoc.fr/articles/10.5802/ojmo.28/
%R 10.5802/ojmo.28
%G en
%F OJMO_2023__4__A7_0
Cafieri, Sonia; Conn, Andrew R.; Mongeau, Marcel. The continuous quadrant penalty formulation of logical constraints. Open Journal of Mathematical Optimization, Tome 4 (2023), article  no. 7, 12 p.. doi: 10.5802/ojmo.28

Cité par Sources :