Safe and tight linear estimators for global optimization

Mathematical Programming

Volumn 102, Issue 3, 2005, Pages 495-517

  Borradaile, Glencora ^a   Van Hentenryck, Pascal ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS; MATHEMATICAL MODELS; NONLINEAR PROGRAMMING; POLYNOMIALS; PROBLEM SOLVING;

LINEAR ESTIMATORS; LINEAR RELAXATION; MULTIVARIATE FUNCTIONS; UNIVARIATE FUNCTIONS;

GLOBAL OPTIMIZATION;

EID: 17444417141     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-004-0533-8     Document Type: Article

References (21)

1. Adjiman, C., Dallwig, S., Floudas, C., Neumaier, A.: A global optimization method, abb, for general twice-differentiable constrained NLPs - I. theoretical advances. Comput. Chem. Engin. 22, 1137-1158 (1998)
2. Benhamou, F., McAllester, D., Van Hentenryck, P.: CLP(Intervals) Revisited. In: Proceedings of the International Symposium on Logic Programming (ILPS-94), Ithaca, NY, Nov. 1994, pp. 124-138
3. Benhamou, F., Older, W.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints. J. Logic Program. 32 (1), 1-24 (1997) July
4. Canny, J.: Some algebraic and geometric computations in pspace. In: Proceedings of the 20th Symposium on the Theory of Computation, 1988, pp. 460-467
5. Garloff, J., Jansson, C., Smith, A.P.: Lower bound functions for polynomials. J. Comput. Appl. Math. 157, 207-225 (2003)
6. Grossmann, I.E., Lee, S.: Generalized convex disjunctive programming: Nonlinear convex hull relaxation. To appear, 2003
7. Hentenryck, P.V., McAllister, D., Kapur, D.: Solving Polynomial Systems Using a Branch and Prune Approach. SIAM J. Numer. Anal. 34 (2), (1997)
8. Jansson, C.: Rigorous error bounds for the optimal value of linear programming problems. In: Proceedings of the First International Workshop on Global Constrained Optimization and Constraint Satisfaction, COCOS 2002, 2003, pp. 59-70
9. Jansson, C.: A rigorous lower bound for the optimal value of convex optimization problems. J. Global Optim. 28 (1), 121-137 (2004)
10. Lebbah, Y., Rueher, M., Michel, C.: A global filtering algorithm for handling systems of quadratic equations and inequations. Lect. Notes Comput. Sci. 2470, 109-123 (2002)
11. Lee, S., Grossmann, I.E.: A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems. Comput, Chem. Engin. 25, 1675-1697 (2001)
12. Lhomme, O.: Consistency Techniques for Numerical Constraint Satisfaction Problems. In: Proceedings of the 1993 International Joint Conference on Artificial Intelligence, Chamberry, France, Aug. 1993
13. McCormick, G.P.: Computability of global solutions to factorable nonconvex programs: Part I - convex underestimating problems. Math. Program. 10, 146-175 (1976)
14. Michel, C., Lebbah, Y., Rueher, M.: Safe embedding of the simplex algorithm in a CSP framework. In: Proceedings CPAIOR'03, 2003, pp. 210-220
15. Neumaier, A., Shcherbina, O.: Safe bounds in linear and mixed-integer programming. To appear
16. Quesada, I., Grossmann, I.E.: A global optimization algorithm for linear fractional and bilinear programs. J. Global Optim. 6, 39-76 (1995)
17. Ryoo, H.S., Sahinidis, N.V.: Global optimization of nonconvex NLPs and MINLPs with applications in process design. Comput. Chem. Engin. 19, 551-566 (1995)
18. Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming, vol 65 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, 2002
19. Van Hentenryck, P., Michel, L., Deville, Y.: Numerica: A Modeling Language for Global Optimization. The MIT Press, Cambridge, MA, USA, 1997
20. Zamora, J.M., Grossmann, I.E.: A comprehensive global optimization approach for the synthesis of heat exchanger networks with no stream splits. Comp. Chem. Engin. 21 (70), S65-S (1997)
21. Zamora, J.M., Grossmann, I.E.: A branch and contract algorithm for problems with concave univariate, bilinear and linear fractional terms. J. Global Optim. 14, 217-249 (1999)