DSpace Collection: Volume 22 Number 3
http://hdl.handle.net/10525/525
Serdica Mathematical Journal Volume 22, Number 3, 1996The Collection's search engineSearch the Channelsearch
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Nontrivial Solutions of Quasilinear Equations In BV
http://hdl.handle.net/10525/616
Title: Nontrivial Solutions of Quasilinear Equations In BV<br/><br/>Authors: Marzocchi, Marco<br/><br/>Abstract: The existence of a nontrivial critical point is proved for a functionalcontaining an area-type term. Techniques of nonsmooth critical point theory are applied.Perturbations of Critical Values in Nonsmooth Critical Point Theory
http://hdl.handle.net/10525/615
Title: Perturbations of Critical Values in Nonsmooth Critical Point Theory<br/><br/>Authors: Degiovanni, M.; Lancelotti, S.<br/><br/>Abstract: The perturbation of critical values for continuous functionals is studied.An application to eigenvalue problems for variational inequalities is provided.<br/><br/>Description: * Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).On a Variational Approach to some Quasilinear Problems
http://hdl.handle.net/10525/614
Title: On a Variational Approach to some Quasilinear Problems<br/><br/>Authors: Canino, Annamaria<br/><br/>Abstract: We prove some multiplicity results concerning quasilinear ellipticequations with natural growth conditions. Techniques of nonsmooth critical pointtheory are employed.Uniform Convergence of the Newton Method for Aubin Continuous Maps
http://hdl.handle.net/10525/613
Title: Uniform Convergence of the Newton Method for Aubin Continuous Maps<br/><br/>Authors: Dontchev, Asen<br/><br/>Abstract: In this paper we prove that the Newton method applied to thegeneralized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued mapF acting in Banach spaces, is locally convergent uniformly in the parameter y ifand only if the map (f +F)^(−1) is Aubin continuous at the reference point. We alsoshow that the Aubin continuity actually implies uniform Q-quadratic convergenceprovided that the derivative of f is Lipschitz continuous. As an application, we givea characterization of the uniform local Q-quadratic convergence of the sequentialquadratic programming method applied to a perturbed nonlinear program.<br/><br/>Description: * This work was supported by National Science Foundation grant DMS 9404431.Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings
http://hdl.handle.net/10525/612
Title: Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings<br/><br/>Authors: Ioffe, Alexander; Penot, Jean-Paul<br/><br/>Abstract: The paper contains calculus rules for coderivatives of compositions,sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentialsin Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials inAsplund spaces and approximate subdifferentials in arbitrary Banach spaces. Thekey element of the unified approach to obtaining various calculus rules for varioustypes of derivatives presented in the paper are simple formulas for subdifferentialsof marginal, or performance functions.Speculating About Mountains
http://hdl.handle.net/10525/611
Title: Speculating About Mountains<br/><br/>Authors: Ribarska, N.; Tsachev, Ts.; Krastanov, M.<br/><br/>Abstract: The definition of the weak slope of continuous functions introduced byDegiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness”of locally Lipschitz functions are discussed. A deformation lemma and a mountainpass theorem for usco mappings are proved. The relation between these resultsand the respective ones for lower semicontinuous functions (cf. [7]) is considered.<br/><br/>Description: ∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology,Bulgaria.∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Scienceand Technology, Bulgaria.Stability of the Iteration Method for non Expansive Mappings
http://hdl.handle.net/10525/610
Title: Stability of the Iteration Method for non Expansive Mappings<br/><br/>Authors: Lemaire, B.<br/><br/>Abstract: The general iteration method for nonexpansive mappings on a Banachspace is considered. Under some assumption of fast enough convergence on thesequence of (“almost” nonexpansive) perturbed iteration mappings, if the basicmethod is τ−convergent for a suitable topology τ weaker than the norm topology,then the perturbed method is also τ−convergent. Application is presented to thegradient-prox method for monotone inclusions in Hilbert spaces.Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces
http://hdl.handle.net/10525/609
Title: Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces<br/><br/>Authors: Azé, D.; Lucchetti, R.<br/><br/>Abstract: To a convex set in a Banach space we associate a convex function(the separating function), whose subdifferential provides useful information on thenature of the supporting and exposed points of the convex set. These points areshown to be also connected to the solutions of a minimization problem involving theseparating function. We investigate some relevant properties of this function and ofits conjugate in the sense of Legendre-Fenchel. Then we highlight the connectionsbetween set convergence, with respect to the slice and Attouch-Wets topologies,and convergence, in the same sense, of the associated functions. Finally, by usingknown results on the behaviour of the subdifferential of a convex function underthe former epigraphical perturbations, we are able to derive stability results forthe set of supported points and of supporting and exposing functionals of a closedconvex subset of a Banach space.<br/><br/>Description: * This work was supported by the CNR while the author was visiting the University of Milan.Epiconvergence D'une Suite De Sommes En Niveaux De Fonctions Convexes
http://hdl.handle.net/10525/608
Title: Epiconvergence D'une Suite De Sommes En Niveaux De Fonctions Convexes<br/><br/>Authors: Traore, S.; Volle, M.<br/><br/>Abstract: We consider the problem of minimizing the max of two convex functionsfrom both approximation and sensitivity point of view.This lead up to studythe epiconvergence of a sequence of level sums of convex functions and the relateddual problems.Somme Ponctuelle D'operateurs Maximaux Monotones
http://hdl.handle.net/10525/607
Title: Somme Ponctuelle D'operateurs Maximaux Monotones<br/><br/>Authors: Attouch, H.; Riahi, H.; Théra, M.<br/><br/>Abstract: The primary goal of this paper is to shed some light on the maximalityof the pointwise sum of two maximal monotone operators. The interesting purposeis to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone operators to the more general setting of reflexiveBanach spaces. In addition, we present some conditions which imply the uniformBrézis-Crandall-Pazy condition. Afterwards, we present, as a consequence, somerecent conditions which ensure the Mosco-epiconvergence of the sum of convexproper lower semicontinuous functions.<br/><br/>Description: ∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernierauteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entreles universités de Marrakech, Rabat et Montpellier.