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Improving inter-block backtracking with interval Newton

Content Provider	Springer Nature Link
Author	Neveu, Bertrand Trombettoni, Gilles Chabert, Gilles
Copyright Year	2009
Abstract	Inter-block backtracking (IBB) computes all the solutions of sparse systems of nonlinear equations over the reals. This algorithm, introduced by Bliek et al. (1998) handles a system of equations previously decomposed into a set of (small) k ×k sub-systems, called blocks. Partial solutions are computed in the different blocks in a certain order and combined together to obtain the set of global solutions. When solutions inside blocks are computed with interval-based techniques, IBB can be viewed as a new interval-based algorithm for solving decomposed systems of nonlinear equations. Previous implementations used Ilog Solver and its IlcInterval library as a black box, which implied several strong limitations. New versions come from the integration of IBB with the interval-based library Ibex. IBB is now reliable (no solution is lost) while still gaining at least one order of magnitude w.r.t. solving the entire system. On a sample of benchmarks, we have compared several variants of IBB that differ in the way the contraction/filtering is performed inside blocks and is shared between blocks. We have observed that the use of interval Newton inside blocks has the most positive impact on the robustness and performance of IBB. This modifies the influence of other features, such as intelligent backtracking. Also, an incremental variant of inter-block filtering makes this feature more often fruitful.
Starting Page	93
Ending Page	116
Page Count	24
File Format	PDF
ISSN	13837133
Journal	Constraints
Volume Number	15
Issue Number	1
e-ISSN	15729354
Language	English
Publisher	Springer US
Publisher Date	2009-05-20
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Intervals Decomposition Solving sparse systems Operations Research/Decision Theory Optimization Computing Methodologies Artificial Intelligence (incl. Robotics)
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Artificial Intelligence Computational Theory and Mathematics Software

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