A new framework for sharp and efficient resolution of NCSP with manifolds of solutions

When numerical CSPs are used to solve systems of n equations with n variables, the preconditioned interval Newton operator plays two key roles: First it allows handling the n equations as a global constraint, hence achieving a powerful contraction. Second it can prove rigorously the existence of sol...

Full description

Saved in:
Bibliographic Details
Published in:Constraints : an international journal Vol. 15; no. 2; pp. 190 - 212
Main Authors: Goldsztejn, Alexandre, Granvilliers, Laurent
Format: Journal Article
Language:English
Published: Boston Springer US 01.04.2010
Springer Verlag
Subjects:
Artificial Intelligence
Computer Science
Numerical Analysis
Operations Research/Decision Theory
Optimization
Interval analysis
Global constraint for under-constrained systems of equations
Preconditioned interval Newton
Branch and prune algorithm
ISSN:1383-7133, 1572-9354
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:When numerical CSPs are used to solve systems of n equations with n variables, the preconditioned interval Newton operator plays two key roles: First it allows handling the n equations as a global constraint, hence achieving a powerful contraction. Second it can prove rigorously the existence of solutions. However, none of these advantages can be used for under-constrained systems of equations, which have manifolds of solutions. A new framework is proposed in this paper to extend the advantages of the preconditioned interval Newton to under-constrained systems of equations. This is achieved simply by allowing domains of the NCSP to be parallelepipeds, which generalize the boxes usually used as domains.
ISSN:1383-7133
1572-9354
DOI:10.1007/s10601-009-9082-3