Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
Algorithm 681: INTBIS, a portable interval Newton/bisection package
ACM Transactions on Mathematical Software (TOMS)
On combining feasibility, descent and superlinear convergence in inequality constrained optimization
Mathematical Programming: Series A and B
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Constraints, consistency and closure
Artificial Intelligence
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
A Global Filtering Algorithm for Handling Systems of Quadratic Equations and Inequations
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
A comparison of complete global optimization solvers
Mathematical Programming: Series A and B
Box-set consistency for interval-based constraint problems
Proceedings of the 2005 ACM symposium on Applied computing
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In this article, a cooperative solution methodology that integrates interval partitioning (IP) algorithms with a local search, feasible sequential quadratic programming (FSQP), is presented as a technique to enhance the solving of continuous constraint satisfaction problems (continuous CSP). FSQP is invoked using a special search tree management system developed to increase search efficiency in finding feasible solutions. In this framework, we introduce a new symbolic method for selecting the subdivision directions that targets immediate reduction of the uncertainty related to constraint infeasibility in child boxes. This subdivision method is compared against two previously established partitioning rules (also parallelized in a similar manner) used in the interval literature and shown to improve the efficiency of IP. Further, the proposed tree management system is compared with tree management approaches that are classically used in IP. The whole method is compared with published results of established symbolic-numeric methods for solving CSP on a number of state-of-the-art benchmarks.