Strong-weak Stackelberg Problems in Finite Dimensional Spaces

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities

Weak Nonlinear Bilevel Problems : Existence of Solutions via Reverse Convex and Convex Maximization Problems

International audienceIn this paper, for a class of weak bilevel programming problems we provide sufficient conditions guaranteeing the existence of global solutions. These conditions are based on the use of reverse convex and convex maximization problems

A Fenchel-Lagrange Duality Approach for a Bilevel Programming Problem with Extremal-Value Function

International audienceIn this paper, for a bilevel programming problem (S) with an extremal-value function, we first give its Fenchel-Lagrange dual problem. Under appropriate assumptions, we show that a strong duality holds between them. Then, we provide optimality conditions for (S) and its dual. Finally, we show that the resolution of the dual problem is equivalent to the resolution of a one-level convex minimization problem

Significantly Increasing the Usability of Model Analysis Tools through Visual Feedback

National audienceA plethora of theoretical results are available which make possible the use of dynamic analysis and model-checking for software and system models expressed in high-level modeling languages like UML, SDL or AADL. Their usage is hindered by the complexity of information processing demanded from the modeler in order to apply them and to effectively exploit their results. Our thesis is that by improving the visual presentation of the analysis results, their exploitation can be highly improved. To support this thesis, we define a trace analysis approach based on the extraction of high-level semantics events from the low-level output of a simulation or model-checking tool. This extraction offers the basis for new types of scenario visualizations, improving scenario understanding and exploration. This approach was implemented in our UML/SysML analyzer and was validated in a controlled experiment that shows a significant increase in the usability of our tool, both in terms of task performance speed and in terms of user satisfaction

Weak linear bilevel programming problems: existence of solutions via a penalty method

AbstractWe are concerned with a class of weak linear bilevel programs with nonunique lower level solutions. For such problems, we give via an exact penalty method an existence theorem of solutions. Then, we propose an algorithm

Méthodes de diagnostic avancées dans la validation formelle des modèles

Malgré l'existence d'un nombre important d'approches et outils de vérification à base de modèles, leur utilisation dans l'industrie reste très limitée. Parmi les raisons qui expliquent ce décalage il y a l'exploitation, aujourd'hui difficile, des résultats du processus de vérification. Dans cette thèse, nous étudions l'utilisation des outils de vérification dans les processus actuels de modélisation de systèmes qui utilisent intensivement la validation à base de modèles. Nous établissons ensuite les limites des approches existantes, surtout en termes d'utilisabilité. A partir de cette étude, nous analysons les causes de l'état actuel des pratiques. Nous proposons une approche complète et outillée d'aide au diagnostic d'erreur qui améliore l'exploitation des résultats de vérification, en introduisant des techniques mettant à profit la visualisation d'information et l'ergonomie cognitive. En particulier, nous proposons un ensemble de recommandations pour la conception d'outils de diagnostic, un processus générique adaptable aux processus de validation intégrant une activité de diagnostic, ainsi qu'un framework basé sur les techniques de l'Ingénierie Dirigée par les Modèles (IDM) permettant une implémentation et une personnalisation rapide de visualisations. Notre approche a été appliquée à une chaîne d'outils existante, qui intègre la validation de modèles UML et SysML de systèmes temps réel critiques. Une validation empirique des résultats a démontré une amélioration significative de l'utilisabilité de l'outil de diagnostic, après la prise en compte de nos préconisations.A plethora of theoretical results are available which make possible the use of dynamic analysis and model-checking for software and system models expressed in high-level modeling languages like UML, SDL or AADL. Their usage is hindered by the complexity of information processing demanded from the modeller in order to apply them and to effectively exploit their results. Our thesis is that by improving the visual presentation of the analysis results, their exploitation can be highly improved. To support this thesis, we define a diagnostic trace analysis approach based on information visualisation and human factors techniques. This approach offers the basis for new types of scenario visualizations, improving diagnostic trace understanding. Our contribution was implemented in an existing UML/SysML analyzer and was validated in a controlled experiment that shows a significant increase in the usability of our tool, both in terms of task performance speed and in terms of user satisfaction. The pertinence of our approach is assessed through an evaluation, based on well-established evaluation mechanisms. In order to perform such an evaluation, we needed to adapt the notion of usability to the context of formal methods usability, and to adapt the evaluation process to our setting. The goal of this experiment was to see whether extending analysis tools with a well-designed event-based visualization would significantly improve analysis results exploitation and the results are meeting our expectations

New necessary and sufficient optimality conditions for strong bilevel programming problems

International audienceIn this paper we are interested in a strong bilevel programming problem (S). For such a problem, we establish necessary and sufficient global optimality conditions. Our investigation is based on the use of a regularization of problem (S) and some well-known global optimization tools. These optimality conditions are new in the literature and are expressed in terms of max–min conditions with linked constraints

Existence of solutions to weak nonlinear bilevel problems

In this paper, which is an extension of [4], we first show the existence of solutions to a class of Min Sup problems with linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel problems. Furthermore, for such a class of bilevel problems, we give a relationship with appropriate d.c. problems concerning the existence of solutions