GOLDSZTEJN , Alexandre

The intervals theory allows constructing supersets of the range of real functions. Therefore, in a very natural way it allows constructing some outer approximation of the solution set of systems of real equations. When it is used in conjnuction to some usual existence theorems (e.g. Brouwer or Miranda theorems), the intervals theory also allows...

Ce papier présente un nouvel algorithme pour la résolution d'une sous-classe de problèmes contraints quantifiés sur le continu (QCSP) pour lesquels les quantificateurs existentiels précèdent les quantificateurs universels. Cette classe de QCSPs possède un remarquable potentiel d'applications dans les domaines de l'ingénierie et de la...

This paper introduces a new algorithm for solving a sub-class 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...

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We investigate the capabilities of constraints programming techniques in rigor- ous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron1, and safe but slow global optimization approaches. We show how constraint program- ming filtering techniques...

The modal intervals theory deals with quantified propositions in AE-form, i.e. universal quantifiers precede existential ones, where variables are quantified over continuous domains and with equality constraints. It allows to manipulate such quantified propositions computing only with bounds of intervals. A simpler formulation of this theory is...

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We investigate the capabilities of constraints programming techniques in rigorous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron, and safe but slow global optimization approaches. We show how constraint programming filtering techniques can...

Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and...

The modal intervals theory deals with quantified propositions in AE-form, i.e. universal quantifiers precede existential ones, where variables are quantified over continuous domains and with equality constraints. It allows to manipulate such quantified propositions computing only with bounds of intervals. A simpler formulation of this theory is...