Laura Scrimali

Solving Strongly Monotone Variational and Quasi-Variational Inequalities

In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequality. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutions. Moreover, we get a new numerical scheme, which rate of convergence is much higher than that of the straightforward gradient method.

Hölder continuity of solutions to elastic traffic network models

This paper aims to study stability and sensitivity analysis for quasi-variational inequalities which model traffic network equilibrium problems with elastic travel demand. In particular, we provide a Hölder stability result under parametric perturbations.

Time-dependent Variational Inequalities and Applications to Equilibrium Problems

We present two different applications of time-dependent variational inequalities. First we propose a new model of time-dependent distributed markets networks which includes delay effects. Afterwards, we deal with time-dependent and elastic models of transportation networks.

A variational inequality formulation of the environmental pollution control problem

In this paper we develop the time-dependent pollution control problem in which different countries aim to determine the optimal investment allocation in environmental projects and the tolerable pollutant emissions, so as to maximize their welfare. We provide the equilibrium conditions governing the model and derive the evolutionary variational inequality formulation. The existence of solutions is investigated and a numerical example is also presented.

Walrasian Equilibrium Problem with Memory Term

The aim of this paper is to study the Walrasian equilibrium problem when the data are time-dependent. In order to have a more realistic model, the excess demand function depends on the current price and on previous events of the market. Hence, a memory term is introduced; it describes the precedent states of the equilibrium. This model is reformulated as an evolutionary variational inequality in the Lebesgue space L2([0,T],ℝ), and, thanks to this characterization, existence and qualitative results on equilibrium solution are given.

The financial equilibrium problem with implicit budget constraints

This paper presents the time-dependent, multi-agent and multi-activity financial equilibrium problem when budget constraints are implicitly defined. Specifically, we assume that total wealth is elastic with respect to the optimal investment. Such a problem is formulated as an infinite dimensional quasi-variational inequality for which an existence result is given.

A solution differentiability result for evolutionary quasi-variational inequalities

We consider a class of evolutionary quasi-variational inequalities arising in the study of some network equilibrium problems. First we prove the existence and uniqueness of solutions and, subsequently, present a differentiability result based on projection arguments.

Evolutionary Quasi-Variational Inequalities and the Dynamic Multiclass Network Equilibrium Problem

We give an existence result to a class of evolutionary quasi-variational inequalities with adaptive set of feasible solutions, where the adaptivity is modeled by solution-dependent equality constraints. A fundamental role will be played by the concept of Mosco convergence related to set-valued applications. Finally, we apply our achievements to the dynamic multiclass network equilibrium problem and provide a numerical example.

Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

In this paper, we develop an infinite dimensional Lagrangian duality framework for modeling and analyzing the evolutionary pollution control problem. Specifically, we examine the situation in which different countries aim at determining the optimal investment allocation in environmental projects and the tolerable pollutant emissions, so as to maximize their welfare. We state the equilibrium conditions underlying the model, and provide an equivalent formulation in terms of an evolutionary variational inequality. Moreover, by means of infinite dimensional duality tools, we prove the existence of Lagrange multipliers that play a fundamental role in order to describe countries’ decision-making processes.

Pollution control quasi-equilibrium problems with joint implementation of environmental projects

Abstract In this paper, we show how one of the Kyoto Protocol mechanisms, the so-called joint implementation in environmental projects, can be transformed into and studied as an infinite-dimensional quasi-variational inequality. Specifically, we examine the situation in which different countries attempt to fulfill Kyoto commitments by investing in emission reduction or emission removal projects in countries where the abatement costs are lower. We derive the equilibrium conditions and prove their characterization in terms of an infinite-dimensional quasi-variational inequality problem. Finally, we discuss the existence of solutions.