Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Population & Approximation algorithm. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Approximation of the viability kernel

Abstract: We study recursive inclusionsxn+1ź G(xn). For instance, such systems appear for discrete finite-difference inclusionsxn+1 źGź(xn) whereGź:=1+źF. The discrete viability kernel ofGź, i.e., the largest discrete viability domain, can be an internal approximation of the viability kernel ofK underF. We study discrete and finite dynamical systems. In the Lipschitz case we get a generalization to differential inclusions of the Euler and Runge-Kutta methods. We prove first that the viability kernel ofK underF can be approached by a sequence of discrete viability kernels associated withxn+1 źźź(xn) whereźź(x) =x + źF(x) + (ML/2) ź2ź. Secondly, we show that it can be approached by finite viability kernels associated withxhn+1 ź (źź(xhn+1) +ź(hź) źXh.

A priori convergence of the greedy algorithm for the parametrized reduced basis method

Abstract: The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the "reduced basis". The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that three greedy algorithms converge; the last algorithm, based on the use of an a posteriori estimator, is the approach actually employed in the calculations.

Impulse differential inclusions: a viability approach to hybrid systems

Abstract: Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approximating their viability and invariance kernels, that is the largest subset that is viable or invariant under the action of the impulse differential inclusion. The results are demonstrated on examples.

Adaptive importance sampling in general mixture classes

Abstract: In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion. The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.

An Overview of ELECTRE Methods and their Recent Extensions

Abstract: We present main characteristics of ELECTRE (ELimination Et Choix Traduisant la REalite - ELimination and Choice Expressing the REality) family methods, designed for multiple criteria decision aiding. These methods use as a preference model an outranking relation on the set of actions—it is constructed in result of concordance and nondiscordance tests involving a specific input preference information. After a brief description of the constructivist conception in which the ELECTRE methods are inserted, we present the main features of these methods. We discuss such characteristic features as the possibility of taking into account positive and negative reasons in the modelling of preferences, without requiring commensurable performance scales; the use of discriminating thresholds for taking into account the imperfect knowledge of data; the absence of systematic compensation between ‘gains’ and ‘losses’. The main weaknesses are also presented. Then, some aspects related to new developments are outlined. These are related to some new methodological developments, new procedures, axiomatic analysis, software tools and several other aspects. This paper is an updated version of a chapter published by the authors under the title ‘ Electre Methods: Main Features and Recent Developments’ in C. Zopounidis and P. Pardalos (Editors): Handbook of Multicriteria Analysis, Springer, Berlin 2010, pp. 51–89. Copyright © 2012 John Wiley & Sons, Ltd.