An efficient and safe framework for solving optimization problems

Journal of Computational and Applied Mathematics

Volumn 199, Issue 2, 2007, Pages 372-377

  Lebbah, Yahia ^a,b   Michel, Claude ^a   Rueher, Michel ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b UNIVERSITY OF ORAN   (Algeria)

Author keywords

Constraint programming; Global optimization; Safe linear relaxations

Indexed keywords

CONSTRAINT PROGRAMMING; LINEAR RELAXATION; SAFE LINEAR RELAXATIONS;

ALGORITHMS; COMPUTATIONAL METHODS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; GLOBAL OPTIMIZATION; LINEAR SYSTEMS;

PROBLEM SOLVING;

EID: 33749656665     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.08.037     Document Type: Article

References (14)

1. C. Audet, Optimisation globale structurée: Propriétés, équivalences et résolution, Ph.D. Thesis, École Polythecnique de Montréal, Montréal, Quebec, 1997.
2. Borradaile G., and Hentenryck P.V. Safe and tight linear estimators for global optimization. Math. Programming 102 3 (2005) 495-517
3. Collavizza H., Delobel F., and Rueher M. Comparing partial consistencies. Reliab. Comput. 5 3 (1999) 213-228
4. E. R. Hansen, Global Optimization Using Interval Analysis. Marcel Dekker, New York, 2004.
5. W. Hock, K. Schittkowski, A comparative performance evaluation of 27 nonlinear programming codes, Computing (1983) 335-358.
6. S. Hongthong, R.B. Kearfott, Rigorous linear overestimators and underestimators, Math. Programming (submitted).
7. Horst R., and Tuy H. Global Optimization: Deterministic Approaches (1993), Springer, New York
8. Kearfott R.B. Rigorous Global Search: Continuous Problems (1996), Kluwer, Dordrecht
9. R. B. Kearfott, Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization, Optimization Methods and Software (submitted).
10. Lebbah Y., Michel C., Rueher M., Merlet J., and Daney D. Efficient and safe global constraints for handling numerical constraint systems. SIAM J. Numer. Anal. 42 5 (2005) 2076-2097
11. A. Neumaier, Complete search in continuous global optimization and constraint satisfaction, Acta Numerica.
12. A. Neumaier, O. Shcherbina, Safe bounds in linear and mixed-integer programming, in Math. Programming A., DOI 10.1007/s10107-003-0433-3.
13. G. Rote, The convergence rate of the sandwich algorithm for approximating convex functions, Computing (1992) 337-361.
14. Sahinidis V., and Twarmalani M. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming (2002), Kluwer, Dordrecht