NEWTON - CONSTRAINT PROGRAMMING OVER NONLINEAR CONSTRAINTS

This paper is an introduction to Newton, a constrain-programming langu age over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (C LP) languages over intervals with advanced interval techniques develop ed in numerical analysis, such as the interval Newton method. Its key conceptual idea is to introduce the notion of box-consistency, which a pproximates are-consistency, a notion well-known in artificial intelli gence. Box-consistency achieves an effective pruning at a reasonable c omputation cost and generalizes some traditional interval operators. N ewton has been applied to numerous applications in science and enginee ring, including nonlinear equation-solving, unconstrained optimization , and constrained optimization. It is competitive with continuation me thods on their equation-solving benchmarks and outperforms the interva l-based methods we are aware of on optimization problems. (C) 1998 Els evier Science B.V.