Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
An incremental constraint solver
Communications of the ACM
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Artificial Intelligence - Special volume on constraint-based reasoning
Modifying the QR-decomposition to constrained and weighted line linear last squares
SIAM Journal on Matrix Analysis and Applications
Lisp and Symbolic Computation
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Solving linear arithmetic constraints for user interface applications
Proceedings of the 10th annual ACM symposium on User interface software and technology
A modular geometric constraint solver for user interface applications
Proceedings of the 14th annual ACM symposium on User interface software and technology
The Cassowary linear arithmetic constraint solving algorithm
ACM Transactions on Computer-Human Interaction (TOCHI)
Dynamic approximation of complex graphical constraints by linear constraints
Proceedings of the 15th annual ACM symposium on User interface software and technology
Algorithms for Constrained and Weighted Nonlinear Least Squares
SIAM Journal on Optimization
Solving non-linear arithmetic constraints in soft realtime environments
Proceedings of the 27th Annual ACM Symposium on Applied Computing
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Constraint programming is a method of problem solving that allows declarative specification of relations among objects. It is important to allow preferences of constraints since it is often difficult for programmers to specify all constraints without conflicts. In this paper, we propose a numerical method for solving nonlinear constraints with hierarcical preferences (i.e., constraint hierarchies) in a least-squares manner. This method finds sufficiently precise local optimal solutions by appropriately processing hierarchical preferences of constraints. To evaluate the effectiveness of our method, we present experimental results obtained with a prototype constraint solver.