Constraint propagation on quadratic constraints

Authors:
Ferenc Domes;Arnold Neumaier
Affiliations:
Faculty of Mathematics, University of Vienna, Vienna, Austria 1090;Faculty of Mathematics, University of Vienna, Vienna, Austria 1090
Venue:
Constraints
Year:
2010

Citing 21
Cited 1

Constraint propagation, relational arithmetic in AI systems and mathematical programs

Annals of Operations Research
Decomposition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems

Computing
Constraint arithmetic on real intervals

Constraint logic programming
CLP(intervals) revisited

ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Presolving in linear programming

Mathematical Programming: Series A and B
Newton—constraint programming over nonlinear constraints

Science of Computer Programming - Special issue on concurrent constraint programming
A gentle introduction to NUMERICA

Artificial Intelligence - Special issue: artificial intelligence 40 years later
The essence of constraint propagation

Theoretical Computer Science
Revising hull and box consistency

Proceedings of the 1999 international conference on Logic programming
PSICO: Solving Protein Structures with Constraint Programming and Optimization

Constraints
Convexification and Global Optimization in Continuous And

Convexification and Global Optimization in Continuous And
Heterogeneous Constraint Solving

ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Enclosing clusters of zeros of polynomials

Journal of Computational and Applied Mathematics
Using Directed Acyclic Graphs to Coordinate Propagation and Search for Numerical Constraint Satisfaction Problems

ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
A Rigorous Global Filtering Algorithm for Quadratic Constraints

Constraints
Interval Analysis on Directed Acyclic Graphs for Global Optimization

Journal of Global Optimization
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques

ACM Transactions on Mathematical Software (TOMS)
GLOPTLAB: a configurable framework for the rigorous global solution of quadratic constraint satisfaction problems

Optimization Methods & Software - GLOBAL OPTIMIZATION
Interval propagation and search on directed acyclic graphs for numerical constraint solving

Journal of Global Optimization
Constraint reasoning in deep biomedical models

Artificial Intelligence in Medicine
Technical Communique: Interval constraint propagation with application to bounded-error estimation

Automatica (Journal of IFAC)

GloMIQO: Global mixed-integer quadratic optimizer

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of univariate quadratic problems. Care is taken to ensure that all methods correctly account for rounding errors in the computations. Various tests and examples illustrate the advantage of the presented method.