Éditeur(s) : HAL CCSDSpringer Résumé : International audience In this chapter, the aim is the solving of variational inclusions fo the form 0_in f(x)+F(x), where f is a subanalytic and locally Lipschitz function, F is a set-valued map with closed graph. The methods are developped using the metric regularity of (f+F) or the Aubin property of (f+F)^{-1}, and often lead to a superlinear convergence. Handbook of optimization, from classical to modern approach
Éditeur(s) : HAL CCSDAcademic Publishing Ltd Résumé : International audience An approximate procedure for solving the problem of nding a zero of a maximal monotone operator is proposed and its convergence is established under various conditions. More precisely, it is shown that this method weakly converges under natural assumptions and strongly converges provided that either the inverse of the involved operator is Lipschitz continuous around zero or the interior of the solution set is nonempty. A particular attention is given to the convex minimization case. AMS Subject Classication : Primary, 90C ; Secondary, 49M45, 65C. ISSN: 1311-8080
Éditeur(s) : HAL CCSDSpringer Résumé : International audience It is known that a locally Lipschitz function f is approximately convex if, and only if, its Clarke subdifferential ∂C f is a submonotone operator. The main object of this work is to extend the above characterization to the class of lower semicontinuous functions. To this end, we establish a new approximate mean value inequality involving three points. We also show that an analogue of the Rockafellar maximal monotonicity theorem holds for this class of functions and we discuss the case of arbitrary subdifferentials Mathematical Programming B
Éditeur(s) : HAL CCSDNorth Atlantic Science Publishing Company Résumé : International audience In this paper, we extend the sensitivity analysis framework developed recently for variational inequalities by Noor and Yen to variational inclusions relying on Wiener-Hopf equation techniques. We prove the continuity and the Lipschitz continuity of the locally unique solution to parametric variational inclusions without assuming differentiability of the given data. ISSN: 1048-9533
Éditeur(s) : HAL CCSD Résumé : International audience Half away between edge detection and object recognition this study aim to characterize singularities in order to guide this two phases. The caracterization is obtained with a generalization of the Lipschitz exponents .for complex structures. This new characterization is called " maxima chain " and integrates the notion of value and spatial repartition of the maxima. The maxima chains are obtained with a multiscale decomposition using a Diadic Discrete Wavelet Transform (DDWT). We use the maxima of the gradient image computed with the wavelet details. The local maxima detect the position of irregular structures (edges) in the image (Canny algorithm). Then we characterize each maxima using their evolution across the different scales. A classification is made using the maxima chains. We integrate the classification to eliminate unwanted maxima (from noise or other objects) to drive the search of closed contours. In fact, there is a totally different signature from one maxima to another depending on the parameters of the objects : nature, shape, size, gray scale, texture, ... RFIA Proceedings Toulouse, France
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