Pia, Stéphane Nicolas
(2009)
Some developments in Preequilibrium and Equilibrium analysis of Variational Inequalities.
[Tesi di dottorato]
(Unpublished)
Item Type: 
Tesi di dottorato

Language: 
English 
Title: 
Some developments in Preequilibrium and Equilibrium analysis of Variational Inequalities 
Creators: 
Creators  Email 

Pia, Stéphane Nicolas  stephane.pia@gmail.com 

Date: 
29 November 2009 
Number of Pages: 
148 
Institution: 
Università degli Studi di Napoli Federico II 
Department: 
Matematica e applicazioni "Renato Caccioppoli" 
Doctoral School: 
Scienze matematiche e informatiche 
PHD name: 
Scienze computazionali e informatiche 
PHD cycle: 
22 
PHD Coordinator: 
name  email 

Ricciardi, Luigi Maria  UNSPECIFIED 

Tutor: 
name  email 

Maugeri, Antonino  maugeri@dmi.unict.it 

Date: 
29 November 2009 
Number of Pages: 
148 
Uncontrolled Keywords: 
Projected Dynamical Systems, Weighted Variational Inequalities, Banach Spaces, Traffic equilibrium problem, preequilibrium problem, Duality, Regularity, Existence, Projection operator in Banach Space. 
MIUR S.S.D.: 
Area 01  Scienze matematiche e informatiche > MAT/05  Analisi matematica Area 01  Scienze matematiche e informatiche > MAT/09  Ricerca operativa Area 01  Scienze matematiche e informatiche > MAT/08  Analisi numerica 
Date Deposited: 
04 Dec 2009 12:47 
Last Modified: 
05 Dec 2014 14:20 
URI: 
http://www.fedoa.unina.it/id/eprint/4150 
DOI: 
10.6092/UNINA/FEDOA/4150 
Abstract
In the present work, the notion of equilibrium and preequilibrium of variational inequalities (but also some for some quasivariational inequalities)is developed in Weighted Hilbert spaces, in strictly convex and smooth Banach spaces and in reflexive Banach spaces. The concept of Weighted variational inequality is introduced, some associated questions as regularity,delayed equilibrium and Lagrangian duality are developed and applied to the traffic equilibrium problem. The more recent notion of preequilibrium very important in time dependent equilibrium must be understood as the optimal path from an arbitrarily point to reach the equilibrium (critical point of the system). The notion of Non pivot and Implicit Dynamical system is introduced, an existence result is given (in Hilbert spaces with linear duality mapping) as application an existence result is given also for a specific quasivariational inequality (translated set) without using the classical assumption for the projection (Lipschitz) [This assumption is wrong a very simple case and a counter example is provided]. The notion of projected dynamical systems is extended to strictly convex and smooth Banach spaces and reflexive Banach spaces and the equivalence between critical points of such PDS and equilibrium of Variational inequalities is proved. Some applications will also be given to the traffic equilibrium problem, an elementary design of an industrial application will be also illustrated.
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