Improved Interval Constraint Propagation for Constraints on Partial Derivatives

Automatic differentiation (AD) automatically transforms programs which calculate elementary functions into programs which calculate the gradients of these functions. Unlike other differentiation techniques, AD allows one to calculate the gradient of any function at the cost of at most 5 values of the function (in terms of time). Interval constraint programming (ICP) is a part of constraint programming focused on representation and processing of nonlinear constraints. We adapt AD to the context of ICP and obtain an algorithm which transforms elementary functions into constraints specifying their gradient. We describe some experiments with implementation of our algorithm in the logic programming language ECLiPSe.