An Efficient Algorithm for a Sharp Approximation of Universally Quantified Inequalities

This paper introduces a new algorithm for solving a subclass of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and design. We propose here a new generic branch and prune algorithm for solving such continuous QCSPs. Standard pruning operators and solution identification operators are specialized for universally quantified inequalities. Special rules are also proposed for handling the parameters of the constraints. First experimentation show that our algorithm outperforms the state of the art methods. Categories and Subject Descriptors G.1 [Numerical Analysis]: Miscellaneous General Terms Theory, Algorithms Keywords Quantified constraints, continuous domains, interval arithmetic

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Alexandre Goldsztejn, Claude Michel, Michel Rueher
• Keywords: Algorithms, Constraint Satisfaction Problems, CORR 2008, Education, Universally Quantified