Access the full text.
Sign up today, get DeepDyve free for 14 days.
H. Schichl, A. Neumaier (2005)
Interval Analysis on Directed Acyclic Graphs for Global OptimizationJournal of Global Optimization, 33
A. Neumaier, O. Shcherbina (2004)
Safe bounds in linear and mixed-integer linear programmingMathematical Programming, 99
A. Facius, R. Lohner (2001)
SCAN 2000: GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics Interval 2000: International Conference on Interval Methods in Science and Engineering Karlsruhe, Germany, September 18–22, 2000Reliable Computing, 7
X-H Vu, D Sam-Haroud, B Faltings (2004)
Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2004)
(1999)
New affine forms in interval branch and bound algorithms
K. Apt (1998)
The Essence of Constraint PropagationTheor. Comput. Sci., 221
L. Jaulin, M. Kieffer, Olivier Didrit, Éric Walter (2001)
Applied Interval Analysis
G. Alefeld, J. Herzberger, J. Rokne (1983)
Introduction to Interval Computation
F. Benhamou, W. Older (1997)
Applying Interval Arithmetic to Real, Integer, and Boolean ConstraintsJ. Log. Program., 32
Safe Bounds in Linear and Mixed-Integer Programming
M Tawarmalani, NV Sahinidis (2002)
Convexification and global optimization in continuous and mixed-integer nonlinear programming. Nonconvex Optimization and Its Applications
A. Neumaier (2004)
Complete search in continuous global optimization and constraint satisfactionActa Numerica, 13
Y Lebbah, M Rueher, C Michel (2003)
Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming (CP 2003)
Yahia Lebbah, M. Rueher, C. Michel (2002)
A Global Filtering Algorithm for Handling Systems of Quadratic Equations and Inequations
F. Benhamou, David McAllester, Pascal Hentenryck (1994)
CLP(Intervals) Revisited
L. Krippahl, P. Barahona (2002)
PSICO: Solving Protein Structures with Constraint Programming and OptimizationConstraints, 7
(2000)
Extensions of affine arithmetic in interval global optimization algorithms
Ramon Moore (1979)
Methods and applications of interval analysis
F. Messine (2002)
Extentions of Affine Arithmetic: Application to Unconstrained Global OptimizationJ. Univers. Comput. Sci., 8
De Figueiredo (1997)
Self-validated numerical methods and applications
Alan Mackworth (1977)
Consistency in Networks of RelationsArtif. Intell., 8
(1983)
Introduction to Interval Computations
Mohit Tawarmalani, N. Sahinidis (2002)
Convexification and Global Optimization in Continuous And
E. Hansen (1975)
A Generalized Interval Arithmetic
(2000)
On the improvement of the division of the affine arithmetic
Xuan-Ha Vu, H. Schichl, Djamila Sam-Haroud (2009)
Interval propagation and search on directed acyclic graphs for numerical constraint solvingJournal of Global Optimization, 45
(2004)
Digital Object Identifier (DOI) 10.1007/s10107-004-0533-8
Luiz Comba, J. Stolfi (1990)
Aane Arithmetic and Its Applications to Computer Graphics
L. Kolev (1998)
A New Method for Global Solution of Systems of Non-Linear EquationsReliable Computing, 4
E. Hansen (1992)
Global optimization using interval analysis, 165
G. McCormick (1983)
Nonlinear Programming: Theory, Algorithms and Applications
RE Moore (1966)
Interval Analysis
G Borradaile, P Hentenryck (2004)
Safe and tight linear estimators for global optimizationMath. Program., 42
J. Garloff, C. Jansson, Andrew Smith (2003)
Lower bound functions for polynomialsJournal of Computational and Applied Mathematics, 157
M. Hanus, M. Artalejo (1996)
Algebraic and Logic Programming: 5th International Conference, ALP '96, Aachen, Germany, September 25 - 27, 1996. Proceedings
Xuan-Ha Vu, Djamila Sam-Haroud, M. Silaghi (2002)
Numerical Constraint Satisfaction Problems with Non-isolated Solutions
ER Hansen (1975)
Interval Mathematics
(2003)
ICOS (Interval Constraints Solver)
S. Miyajima, Takatomi Miyata, M. Kashiwagi (2003)
A New Dividing Method in Affine ArithmeticIEICE Trans. Fundam. Electron. Commun. Comput. Sci., 86-A
Olivier Lhomme (1993)
Consistency Techniques for Numeric CSPs
(2009)
Rigorous linear overestimators and underestimators
F. Benhamou (1996)
Heterogeneous Constraint Solving
Ralph Martin, Huahao Shou, I. Voiculescu, A. Bowyer, Guojin Wang (2002)
Comparison of interval methods for plotting algebraic curvesComput. Aided Geom. Des., 19
P. Pardalos, S. Mishra, Shouyang Wang, K. Lai (2008)
Nonconvex Optimization and Its Applications
Xuan-Ha Vu, Djamila Sam-Haroud, B. Faltings (2004)
Combining multiple inclusion representations in numerical constraint propagation16th IEEE International Conference on Tools with Artificial Intelligence
F Benhamou, D McAllester, P Hentenryck (1994)
Proceedings of the International Logic Programming Symposium
Laurent Granvilliers, F. Benhamou (2006)
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniquesACM Trans. Math. Softw., 32
L. Kolev (2004)
An Improved Interval Linearization for Solving Nonlinear ProblemsNumerical Algorithms, 37
Mohit Tawarmalani, N. Sahinidis (2002)
Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
A. Neumaier (1990)
Interval methods for systems of equations
F. Benhamou, F. Goualard, Laurent Granvilliers, J. Puget (1999)
Revising Hull and Box Consistency
C. Jansson (2000)
Convex-Concave ExtensionsBIT Numerical Mathematics, 40
Pascal Hentenryck, L. Michel, Y. Deville (1997)
Numerica: A Modeling Language for Global Optimization
L. Kolev (2001)
Automatic Computation of a Linear Interval EnclosureReliable Computing, 7
G. McCormick (1976)
Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problemsMathematical Programming, 10
(2003)
Global filtering algorithms based on linear relaxations. In: Notes of the 2nd International Workshop on Global Constrained Optimization and Constraint Satisfaction (COCOS
Building tight and conservative enclosures of the solution set is of crucial importance in the design of efficient complete solvers for numerical constraint satisfaction problems (NCSPs). This paper proposes a novel generic algorithm enabling the cooperative use, during constraint propagation, of multiple enclosure techniques. The new algorithm brings into the constraint propagation framework the strength of techniques coming from different areas such as interval arithmetic, affine arithmetic, and mathematical programming. It is based on the directed acyclic graph (DAG) representation of NCSPs whose flexibility and expressiveness facilitates the design of fine-grained combination strategies for general factorable systems. The paper presents several possible combination strategies for creating practical instances of the generic algorithm. The experiments reported on a particular instance using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming illustrate the flexibility and efficiency of the approach.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Mar 18, 2009
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.