Displaying similar documents to “Economic equilibrium through variational inequalities”

A note on economic equilibrium with nonsatiated utility functions

Magdalena Nockowska-Rosiak (2013)

Applicationes Mathematicae

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The purpose of this paper is to prove the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with positive price vector with nonsatiated utility functions of consumers by using variational inequalities. Moreover, the same technique is used to give an alternative proof of the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with nonnegative, nonzero price vector with nonsatiated utility functions. ...

Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo, Carlos F. Leal, Cecília S. Pinto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified...

A Survey on Vector Variational Inequalities

F. Giannessi, G. Matroeni, X. Q. Yang (2009)

Bollettino dell'Unione Matematica Italiana

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The paper consists in a brief overview on Vector Variational Inequalities (VVI). The connections between VVI and Vector Optimization Problems (VOP) are considered. This leads to point out that necessary optimality conditions for a VOP can be formulated by means of a VVI when the objective function is Gâteaux differentiable and the feasible set is convex. In particular, the existence of solutions and gap functions associated with VVI are analysed. Gap functions provide an equivalent formulation...

Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets

Alexander Kaplan, Rainer Tichatschke (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the "feasible" set as well as the operator of the variational inequality.

The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory

Ammar Derbazi, Mohamed Dalah, Amar Megrous (2016)

Applications of Mathematics

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We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field...

Variational inequalities in noncompact nonconvex regions

Ching-Yan Lin, Liang-Ju Chu (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem...