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

“…The theory of quasi-variational inequalities has now established itself as one of the most promising areas of applied mathematics, offering a powerful mathematical apparatus for investigating a broad range of problems arising in diverse disciplines. Applications of quasivariational inequalities can be found in material science [12], equilibrium models [2,22], financial models [6], frictional elastostatic contact [19], image processing [16], sand-piles formation [3], and numerous others.…”

Section: Introductionmentioning

confidence: 99%

Inverse problems for quasi-variational inequalities

Khan

Motreanu

2017

J Glob Optim

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In this short note, our aim is to investigate the inverse problem of parameter identification in quasi-variational inequalities. We develop an abstract nonsmooth regularization approach that subsumes the total variation regularization and permits the identification of discontinuous parameters. We study the inverse problem in an optimization setting using the output-least squares formulation. We prove the existence of a global minimizer and give convergence results for the considered optimization problem. We also discretize the identification problem for quasi-variational inequalities and provide the convergence analysis for the discrete problem. We give an application to the gradient obstacle problem.

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Restricted Participation on Financial Markets: A General Equilibrium Approach Using Variational Inequality Methods

2020

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We deal with the analysis of a general equilibrium model with restricted participation in financial markets and with numeraire assets. We consider an exchange economy and assume that there are two periods of time and S possible states of nature in the second period. Markets may in principle be complete, but each household has her own specific restricted way to access to it. In particular, we assume that households are allowed to choose portfolios in a closed and convex set containing zero. Our main goal in this work is to provide a proof of existence of equilibria under relatively general assumptions, by assuming that the households may have non-complete or non-transitive preferences, and by using a variational inequality approach. More precisely, we introduce a sequence of generalized quasi-variational inequalities and we show that an associated sequence of solutions converges to an equilibrium.

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

Cited by 7 publications

References 38 publications

The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints

The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints

Inverse problems for quasi-variational inequalities

Restricted Participation on Financial Markets: A General Equilibrium Approach Using Variational Inequality Methods

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