QUAD-CLP(R): Adding the Power of Quadratic Constraints

. We report on a new way of handling non-linear arithmetic constraints and its implementation into the QUAD-CLP(R) language. Important properties of the problem at hand are a discretization through geometric equivalence classes and decomposition into convex pieces. A case analysis of those equivalence classes leads to a relaxation (and sometimes recasting) of the original constraints into linear constraints, much easier to handle. Complementing earlier expositions in [18] and [19], the present focus is on applications upholding its worth. 1. Motivation. This paper presents the constraint programming language QUAD-CLP(R) which offers a powerful novel solving strategy for non-linear arithmetic constraints under the computing paradigm of logic programming. Emphasis will be given here to the techniques involved in the constraint solver for quadratic constraints over R and to applications making use of this added power. Despite the enormous potential of non-linear arithmetic constraints in..