61 research outputs found
Characterizations of -well-posedness for parametric quasivariational inequalities defined by bifunctions
The purpose of this paper is to investigate the
well-posedness issue of parametric quasivariational inequalities
defined by bifunctions. We generalize the concept of
-well-posedness to parametric quasivariational inequalities
having a unique solution and derive some characterizations of
-well-posedness. The corresponding concepts of
-well-posedness in the generalized sense are also introduced
and investigated for the problems having more than one solution.
Finally, we give some sufficient conditions for
-well-posedness of parametric quasivariational inequalities
Well-posedness for generalized mixed vector variational-like inequality problems in Banach space
In this article, we focus to study about well-posedness of a generalized mixed vector variational-like inequality and optimization problems with aforesaid inequality as constraint. We establish the metric characterization of well-posedness in terms of approximate solution set.Thereafter, we prove the sufficient conditions of generalized well-posedness by assuming the boundedness of approximate solution set. We also prove that the well-posedness of considered optimization problems is closely related to that of generalized mixed vector variational-like inequality problems. Moreover, we present some examples to investigate the results established in this paper
Including Social Nash Equilibria in Abstract Economies
We consider quasi-variational problems (variational problems having constraint sets depending on their own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. First, using an extension of the classical Minty lemma, we show that new upper stability results can be obtained for parametric quasi-variational and linearized quasi-variational problems, while lower stability, which plays a fundamental role in the investigation of hierarchical problems, cannot be achieved in general, even on very restrictive conditions. Then, regularized problems are considered allowing to introduce approximate solutions for the above problems and to investigate their lower and upper stability properties. We stress that the class of quasi-variational problems include social Nash equilibrium problems in abstract economies, so results about approximate Nash equilibria can be easily deduced.quasi-variational, social Nash equilibria, approximate solution, closed map, lower semicontinuous map, upper stability, lower stability
Well-posedness for generalized mixed vector variational-like inequality problems in Banach space
In this article, we focus to study about well-posedness of a generalized mixed vector variational-like inequality and optimization problems with aforesaid inequality as constraint. We establish the metric characterization of well-posedness in terms of approximate solution set.Thereafter, we prove the sufficient conditions of generalized well-posedness by assuming the boundedness of approximate solution set. We also prove that the well-posedness of considered optimization problems is closely related to that of generalized mixed vector variational-like inequality problems. Moreover, we present some examples to investigate the results established in this paper
Stability of the solution set of quasi-variational inequalities and optimal control
For a class of quasi-variational inequalities (QVIs) of obstacle-type the
stability of its solution set and associated optimal control problems are
considered. These optimal control problems are non-standard in the sense that
they involve an objective with set-valued arguments. The approach to study the
solution stability is based on perturbations of minimal and maximal elements of
the solution set of the QVI with respect to {monotone} perturbations of the
forcing term. It is shown that different assumptions are required for studying
decreasing and increasing perturbations and that the optimization problem of
interest is well-posed.Comment: 29 page
Parametric well-posedness for variational inequalities defined by bifunctions
AbstractIn this paper we introduce the concepts of parametric well-posedness for Stampacchia and Minty variational inequalities defined by bifunctions. We establish some metric characterizations of parametric well-posedness. Under suitable conditions, we prove that the parametric well-posedness is equivalent to the existence and uniqueness of solutions to these variational inequalities
Variational Inequalities in Critical-State Problems
Similar evolutionary variational inequalities appear as convenient
formulations for continuous quasistationary models for sandpile growth,
formation of a network of lakes and rivers, magnetization of type-II
superconductors, and elastoplastic deformations. We outline the main steps of
such models derivation and try to clarify the origin of this similarity. New
dual variational formulations, analogous to mixed variational inequalities in
plasticity, are derived for sandpiles and superconductors.Comment: Submitted for publicatio
Gap functions and error bounds for variational-hemivariational inequalities
In this paper we investigate the gap functions and regularized gap functions for a class of variational–hemivariational inequalities of elliptic type. First, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the variational–hemivariational inequalities. Then, the global error bounds for such inequalities in terms of regularized gap functions are derived by using the properties of the Clarke generalized gradient. Finally, an application to a stationary nonsmooth semipermeability problem is given to illustrate our main results
α
The concepts of α-well-posedness, α-well-posedness in the
generalized sense, L-α-well-posedness and L-α-well-posedness in the generalized sense for
mixed quasi variational-like inequality problems are investigated. We present some metric
characterizations for these well-posednesses
- …