Sofia Giuffrè

General infinite dimensional duality and applications to evolutionary network equilibrium problems

In this paper the authors present an infinite dimensional duality theory for optimization problems and evolutionary variational inequalities where the constraint sets are given by inequalities and equalities. The difficulties arising from the structure of the constraint set are overcome by means of generalized constraint qualification assumptions based on the concept of quasi relative interior of a convex set. An application to a general evolutionary network model, which includes as special cases traffic, spatial price and financial equilibrium problems, concludes the paper.

Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery

Without using a technical language, but using the universal language of mathematics, we provide simple but significant laws, as Deficit Formula, Balance Law and Liability Formula, for the management of the world economy. Decisions, under these laws, for the recovery of the economy and for the good governance clearly appear. Further a simple but useful economical indicator E(t) is provided and the results are illustrated with a significant example.

Duality Theory and Applications to Unilateral Problems

This paper is concerned with the problem of strong duality between an infinite dimensional convex optimization problem with cone and equality constraints and its Lagrange dual.A necessary and sufficient condition and sufficient conditions, really new, in order that the strong duality holds true are given. As an application, the existence of the Lagrange multiplier associated with the obstacle problem and to an elastic–plastic torsion problem, more general than the ones previously considered, is stated together with a characterization of the elastic–plastic torsion problem. This application is the main result of the paper.It is worth remarking that the usual conditions based on the interior, on the core, on the intrinsic core or on the strong quasi-relative interior cannot be used because they require the nonemptiness of the interior (and of the above mentioned generalized interior concepts) of the ordering cone, which is usually empty.

Some classes of projected dynamical systems in Banach spaces and variational inequalities

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.

Random Variational Inequalities and the Random Traffic Equilibrium Problem

In the paper we study, in a Hilbert space setting, a general random traffic equilibrium problem and characterize the random Wardrop equilibrium distribution by means of a random variational inequality. Some existence results are provided and the associated Lagrange function is studied. Some examples illustrate the random variational inequality and the counterintuitive behaviour of the traffic equilibrium problem is focused.

Weighted Traffic Equilibrium Problem in Non Pivot Hilbert Spaces with Long Term Memory

In the paper we consider a weighted traffic equilibrium problem in a non‐pivot Hilbert space and prove the equivalence between a weighted Wardrop condition and a variational inequality with long term memory. As an application we show, using recent results of the Senseable Laboratory at MIT, how wireless devices can be used to optimize the traffic equilibrium problem.

Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem

This paper is concerned with a general model of financial flows and prices related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. In particular, using delicate tools of Functional Analysis, besides existence results of financial equilibrium, in the dual formulation, the Lagrange functions

Lagrange multipliers in elastic-plastic torsion

\rho _j^{*1}(t)