Stephane Pia - Academia.edu (original) (raw)
Papers by Stephane Pia
A Panoramic View on Projected Dynamical Systems
Springer Optimization and Its Applications, 2009
The theory of generalized projections both in non-pivot Hilbert spaces and strictly convex and sm... more The theory of generalized projections both in non-pivot Hilbert spaces and strictly convex and smooth Banach spaces is developed and the related theory of projected dynamical systems is highlighted. A particular emphasis is given to the equivalence between solutions of variational inequality and critical points of projected dynamical systems.
Journal of Function Spaces and Applications, 2012
This paper presents a generalization of the concept and uses of projected dynamical systems to th... more This paper presents a generalization of the concept and uses of projected dynamical systems to the case of nonpivot Hilbert spaces. These are Hilbert spaces in which the topological dual space is not identified with the base space. The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.
Nonlinear Analysis: Theory, Methods & Applications, 2009
We introduce a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the eq... more We introduce a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the equivalence between a weighted Wardrop condition and a variational inequality. As an application we show, using some recent results of the Senseable Laboratory at MIT, how wireless devices can be used to optimize the traffic equilibrium problem.
Journal of Optimization Theory and Applications, 2005
In this paper, we make explicit the connection between projected dynamical systems on Hilbert spa... more In this paper, we make explicit the connection between projected dynamical systems on Hilbert spaces and evolutionary variational inequalities. We give a novel formulation that unifies the underlying constraint sets for such inequalities, which arise in time-dependent traffic network, spatial price, and a variety of financial equilibrium problems. We emphasize the importance of the results in applications and provide a traffic network numerical example in which we compute the curve of equilibria.
Competitive financial equilibrium problems with policy interventions
Journal of Industrial & Management Optimization, 2005
ABSTRACT An evolutionary model is presented for a multi–sector, multi–instrument financial equili... more ABSTRACT An evolutionary model is presented for a multi–sector, multi–instrument financial equilibrium problem, with general utility function and including policy interventions in the form of taxes and price controls. We give the evolutionary financial equilibrium condition, prove an equivalent variational inequality formulation, from which an existence result follows.
Journal of Global Optimization, 2007
We introduce some Projected Dynamical Systems based on metric and generalized Projection Operator... more We introduce some Projected Dynamical Systems based on metric and generalized Projection Operator in a strictly convex and smooth Banach Space. Then we prove that critical points of these systems coincide with the solution of a Variational Inequality.
Duality for Weighted Traffic Equilibrium Problem and Computational Procedure
AIP Conference Proceedings, 2009
We consider the weighted traffic equilibrium problem introduced in [4] and we apply the infinite-... more We consider the weighted traffic equilibrium problem introduced in [4] and we apply the infinite-dimensional duality theorem developed in [2], obtaining the existence of Lagrange variables, which allow to describe the behavior of the weighted traffic. Moreover, making use of a regularity result we present a descritization method to compute the weighted traffic equilibrium solution.
A Panoramic View on Projected Dynamical Systems
Springer Optimization and Its Applications, 2009
The theory of generalized projections both in non-pivot Hilbert spaces and strictly convex and sm... more The theory of generalized projections both in non-pivot Hilbert spaces and strictly convex and smooth Banach spaces is developed and the related theory of projected dynamical systems is highlighted. A particular emphasis is given to the equivalence between solutions of variational inequality and critical points of projected dynamical systems.
Journal of Function Spaces and Applications, 2012
This paper presents a generalization of the concept and uses of projected dynamical systems to th... more This paper presents a generalization of the concept and uses of projected dynamical systems to the case of nonpivot Hilbert spaces. These are Hilbert spaces in which the topological dual space is not identified with the base space. The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.
Nonlinear Analysis: Theory, Methods & Applications, 2009
We introduce a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the eq... more We introduce a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the equivalence between a weighted Wardrop condition and a variational inequality. As an application we show, using some recent results of the Senseable Laboratory at MIT, how wireless devices can be used to optimize the traffic equilibrium problem.
Journal of Optimization Theory and Applications, 2005
In this paper, we make explicit the connection between projected dynamical systems on Hilbert spa... more In this paper, we make explicit the connection between projected dynamical systems on Hilbert spaces and evolutionary variational inequalities. We give a novel formulation that unifies the underlying constraint sets for such inequalities, which arise in time-dependent traffic network, spatial price, and a variety of financial equilibrium problems. We emphasize the importance of the results in applications and provide a traffic network numerical example in which we compute the curve of equilibria.
Competitive financial equilibrium problems with policy interventions
Journal of Industrial & Management Optimization, 2005
ABSTRACT An evolutionary model is presented for a multi–sector, multi–instrument financial equili... more ABSTRACT An evolutionary model is presented for a multi–sector, multi–instrument financial equilibrium problem, with general utility function and including policy interventions in the form of taxes and price controls. We give the evolutionary financial equilibrium condition, prove an equivalent variational inequality formulation, from which an existence result follows.
Journal of Global Optimization, 2007
We introduce some Projected Dynamical Systems based on metric and generalized Projection Operator... more We introduce some Projected Dynamical Systems based on metric and generalized Projection Operator in a strictly convex and smooth Banach Space. Then we prove that critical points of these systems coincide with the solution of a Variational Inequality.
Duality for Weighted Traffic Equilibrium Problem and Computational Procedure
AIP Conference Proceedings, 2009
We consider the weighted traffic equilibrium problem introduced in [4] and we apply the infinite-... more We consider the weighted traffic equilibrium problem introduced in [4] and we apply the infinite-dimensional duality theorem developed in [2], obtaining the existence of Lagrange variables, which allow to describe the behavior of the weighted traffic. Moreover, making use of a regularity result we present a descritization method to compute the weighted traffic equilibrium solution.